Abstract
As the memristor device is asymmetrical in nature, it is not a bilateral element like the resistor in terms of circuit functionality. Thus, it causes hindrance in some memristor-based applications such as in cellular nonlinear network neighborhood connections and in some application areas where its orientation is essentially expected to act as a bilateral circuit element reliable for bidirectional communication, for example, in signal and image processing or in electrical synapse devices. We introduce a memristor-based network for each purpose where we replace the conventional series resistances by memristors. The memristor asymmetry is described from the circuit point of view allowing us to observe its interaction within the network. Moreover, a memristor fuse is proposed in order to achieve the memristive effect with symmetry, which is formed basically by connecting two memristors antiserially. We, therefore, analyze the memristor fuse from its basic principle along with the theoretical analysis and then observe the response from the circuit point of view.
1 Introduction
The memristor was predicted in 1971 (Chua) by observing the symmetrical nature of the three known basic circuit elements, resistor R, capacitor C, and inductor L, with respect to the four circuit variables, namely, electric voltage v, electric current i, electric charge q, and magnetic flux ϕ, see Figure 1. As stated in the work of for the sake of completeness, there should be a fourth passive circuit element describing the relationship between magnetic flux ϕ and electric charge q, hence named memristor. A broader class of this device known as the memristive system is given by . Memristor (M) is the short form of memory resistor, this name being due to the fact that the device remembers its previous history (resistance), hence the memory effect, and is analogous to a resistor with memory. Depending on the type of excitation, a memristor can be described as charge controlled or flux controlled () which are preferably described as memristance and memductance, having unit as Ohms () and Siemens (S), respectively.
FIGURE 1
For more than 3 decades, memristor remained a mystery until in 2008 () a group of researchers from the HP laboratory announced the successful realization of the first solid-state memristor in a device form (). This recent discovery of the HP lab allured many scientists, engineers, and researchers to explore the feasible applications of memristor in discrete and crossbar array configurations and more possible device technologies.
Since the invention by , many memristor technologies emerged which are basically adhered to the principle of bipolar resistance switching between two extreme values, namely, and that, respectively, correspond to the lowest and highest resistance state of the device. Note that another commonly used memristor technology is the self-directed channel device () whose conductivity is based on the formation and dissolution of ionic bridges that result in low and high resistance states, respectively, but we will mainly refer to the TiO2 memristor in the remaining part of this article. Figure 2 shows the formation of the titanium-oxide memristor with the TiO2 doped with some positive oxygen vacancies. Hence, the TiO2 memristor is an example of MIM devices, i. e., metal–insulator–metal, in which a thin bilayer of TiO2 film is sandwiched between platinum electrodes (labeled as and ). The small positive spots in the doped region refer to the positive charges due to the oxygen vacancies (; ).
FIGURE 2
The mathematical description of the titanium-oxide memristor when a positive voltage is applied to the 2-port device shown in Figure 2A corresponds to a current flowing into the memristor, while the voltage is shared in two parts: a voltage across the doped region (the left part of Figure 2A) and the complementary part present across the undoped region (the right part of Figure 2A). Let us consider the oxygen vacancies in the doped region. These charge carriers with mass m and charge q are accelerated by the electric field and are broken as they collide together. They finally reach a limit speed , where is the mean time between two consecutive collisions, leading to their averaged velocity , where is the mobility of the oxygen vacancies. They expand the doped region toward the right (), whose boundary increases with a positive current such that . Finally, with the normalized form , the behavior of the memristor is given bywhere is the memristance and is the difference between and Ron. When integrating (1c) for x from 0 to 1,where is the charge required to move completely the doped/undoped boundary from to . Then, Eq. 1c can be rewritten as
A window function is often introduced as a factor in the right-hand side of Eq. 3 for nonlinear dopant drift modeling, i.e., to avoid x from taking values outside of the interval (), to give
Eq. 1 characterizes a bipolar memristor where the resistance switching depends on the voltage polarity (, , ). However, there are other reported memristors exhibiting symmetry in polarity, such as unipolar, nonpolar, and complementary resistive switching memristors (, , , ). Here, the resistance switching between and (and vice versa) can be completed in the same voltage polarity. As such, unipolar memristors are important elements in memory arrays and logic circuit implementation ().
Many memristor-based applications are reported (, , including implementation of chaotic circuits and field programmable gate array (, ), high-density memory and data storage (, ), cellular neural networks (, ), neuromorphicmemristance for one system (, ), and logic circuits (, ). A memristor is reported to be a promising element as synapse owing to its flexibility in conductance modulation and very effective high-density connectivity , , . There are many implemented electronic memristor-based synapses for various neumorphic computing architectures (, , , , , , ).
The interesting features of memristors, such as connection flexibility, nanoscaleability, memory capability, and conductance modulation, are essential properties affirming the reliability of the memristor in neuromorphic networks, especially as synaptic function. The memristor is studied in the coupling mode between two neuron cells where the synchronization phenomena is investigated numerically and theoretically (, , , ). Unidirectional coupling and bidirectional or mutual coupling are the commonly used coupling modes for nonlinear chaotic systems (). The synchronization and chaos between two neuron cells is also investigated by using unidirectional and bidirectional coupling ().
The main application of our work is to use the memristor as a synaptic link between neurons in electronic models, as for example, in hybrid technologies with neuronal electronic prosthesis between real neurons. The network is initially composed of a linear capacitor and a nonlinear resistance in each cell and a linear resistor in series (), see Figure 3A. The equivalent memristor-based network is shown in Figure 3B where the series resistance is replaced by a memristor. The memory circuit element being intrinsically asymmetric (), the TiO2 memristor crossbar is used to visualize the nature of current flowing through the device with respect to the polarities of the applied voltage. Using a memristor for the image processing technique was also reported by , where a memristive grid is employed to perform edge detection. In a first step to implement 2D-memristor–based cellular nonlinear networks for signal and image processing purposes or for modeling a neural network with memristors as synapses, we rather focus here on the interaction of the memristor between pixel cells by considering a system of two cells in order to assess the behavior of the memristor quantitatively and qualitatively.
FIGURE 3
The underlining task is accompanied by observing the pinched hysteresis loop (PHL), memristance transition, voltage evolution of the cells, and the explanation of the memristor’s lack of bilaterality. We derive analytically a second-order nonlinear differential equation characterizing the interaction of the memristor between the two cells bidirectionally. The system is studied in the phase plane allowing visualizing the memristor asymmetry. The memristance variation of a bipolar memristor with respect to the direction of flowing current affects its reliability in some potential applications where sensitivity in direction is important, for example, the memristive grid for neuromorphic application and image processing, hence the need for the so-called memristor fuse (). The formation is achieved by connecting two identical memristors antiserially. We describe the memristor fuse and obtain some results in accordance to our application.
2 Description of the Polarity Reversal
Figures 4A,B show two identical memristors and connected in parallel across a voltage source V with terminals for a direct polarization for but reversed in the case of , both memristors having the same initial condition. The schematic is shown in a way to illustrate the trending of the mobile charge carriers under the influence of external bias. The currents through and are measured as and , respectively, and . Although the memristors are identical, we found that ; hence, the conductivity differs if the polarity is reversed, even though with the same initial condition and voltage excitation. Hence, the device offers low resistance path with the orientation of and high resistance path for that of .
FIGURE 4
The schematic is shown in Figure 2A, where initially, the width of TiO2 altogether is D and the width of the doped (TiO2-e) region is w and the undoped one is . Figure 4A shows that the positive charges in the doped region are repelled by the positive terminal of the power supply, thereby making the width of the doped region to expand such that , as illustrated by the width trending . If the terminals of the applied voltage are reversed (Figure 4B), the negative terminal from the power supply attracts the positive charges in the doped region, thereby causing the contraction of the doped region such that with the width trending illustrated as . Figure 4C shows the comparison of the current flowing through and with respect to the applied voltage source. The result is obtained using a sine input voltage source and a window function by . The current and have different absolute values. The current–voltage graph of falls in the second and fourth quadrants due to the reversed terminals of .
It follows that the conductivity of a memristor can be compared to that of a diode in terms of terminal polarity. However, unlike the diode, the memristor conducts electricity in both directions but the conductivity increases if its higher polarity terminal is connected to the positive terminal of the applied voltage source and decreases if its lower polarity terminal is connected to the positive terminal of the applied input voltage source.
In a nanoscale device, even small voltages can generate large electric field required to cause current to flow through the device. The smaller the device, the higher the electric field developed, and hence, more current flows through the device (). The electroforming process forms the oxygen vacancies which cause a high-conducting channel (TiO2-e) shunting the bulk of the insulation film TiO2 (, ). Depending on the nature of the bipolar input source, the conducting channel is affected by the variation of the tunneling barrier width (). Therefore, the device conductivity can be described by the Simmons tunneling barrier model (, , ), devoted to the conduction of a material in a given medium. Depending on the magnitude of the input source, the boundary moves back and forth proportionally to the concentration of the dopant, thus setting the resistance of the memristor. Note that, in Figure 2, in reality, the boundary can never be outside of the interval because there is always doped and undoped material present; in other words, the doped region can only expand or contract but never ceases to exist.
3 Memristor Asymmetry From the Circuit Point of View
To vividly visualize the effect of memristor asymmetry, we consider two identical RC cells shown in
Figure 5, which is the simplified setup of the system in the work of
. The cells are labeled as cell-1 and cell-2 having potentials
and
, respectively, coupled together by a memristor
Mwith its orientation as shown. Two tests are carried out which allow to observe the interaction of the memristor bidirectionally:
1. Cond-1:
2. Cond-2:
FIGURE 5
In the former, the direction of is as shown in Figure 5; meanwhile, in the latter, the direction is reversed. The voltage across the memristor is for Cond-1 and for Cond-2. By taking into account the history of the memristor, we havewhere is the amount of charge already flowed through the device from its last usage, and thus, it becomes the initial charge at time . Therefore, we consider the same memristor M with the same previous history, characterized by the initial charge . In Cond-1, it is placed in one way as shown in Figure 5 and in Cond-2, on the opposite way.
Figure 5 is simulated in SPICE using the memristor model by , which can easily be implemented experimentally. The setup is activated by closing the switches and simultaneously. For each Cond-1 and Cond-2, we considered the initial charge ; meanwhile, the low and high resistance limits of the memristor are and , respectively (). Given the initial conditions of the cells, that is, for Cond-1, , and for Cond-2, , , the result is shown in Figure 6. It is, however, important to note that the initial voltages can have any numerical values. Figure 6A shows the memristance transition for Cond-1 and Cond-2, illustrated, respectively, by the solid and dash curves. Figure 6B shows the corresponding time evolution of and . The results show that Cond-1 and Cond-2 lead to quite different scenarios.
FIGURE 6
In Cond-1, the memristance decreases corresponding to the expansion of the doped region; meanwhile, for Cond-2, the memristance increases corresponding to the contraction of the doped region. In both Cond-1 and Cond-2, the memristance transition eventually flattens as the cells stabilize, that is, at a time when . The memristance transition depends on the initial conditions of the cells. For example, Figure 7 shows the case where the initial conditions of the cells are changed with two different initial charges as and . Figure 7A and 7B, respectively, show the memristance transition and the corresponding voltage evolution of the cells. Furthermore, Figure 6B and 7B show that the orientation of the memristor according to Cond-1 or Cond-2 affects the time taken for the system to stabilize. Let represent the voltage across memristor; hence, for Cond-1 and Cond-2. No current flows through the memristor when because the voltage across the memrisor is also zero even though , see Figure 8. The combined evolution of and eventually stabilizes to zero due to the resistive nature of the cells.
FIGURE 7
FIGURE 8
Furthermore, from Figure 5, one can deduce the following equations:where is defined in the work of as follows:with if and if . The dynamics of the memristor between the two cells can be expressed analytically. Eqs. 6–8 are simplified to givewhere is the time constant of the cell. Substituting Eq. 9 into 11 and taking the time derivative on the left-hand side give
Eq. 12 can be expressed in a normalized form aswhere is the normalized time, is the normalized charge (, ), is the first derivative of X with respect to τ, is the second derivative of X with respect to τ, and is the normalized form of (10), thus rewritten as follows:with . Substituting (14) into (13) and posing and , Eq. 13 is better studied when replaced by the set of equationsallowing to study the system in the phase plane (X,Y) which facilitates the observation of cell interaction in relation to the memristive effect under different initial conditions. Furthermore, Eq. 13 requires a continuous first derivative of with respect to X at and , and it is achieved perfectly by using Eq. 14. The history of a memristor marks its initial value in ohms, determined by the last amount of electric charge passed through it. However, it is reported in the work of and that the initial memristance is unknown. It is important to note that the state is not fixed (in other words, it is unknown) and it strongly depends on the history of the device. Moreover, from Eq. 15, we getwhere H is a conservative expression for the equation set Eq. 15, only depending on the initial conditions , , , and . Hence, , being simply the normalized form of , and we obtained from Eq. 9 as follows:
Recall that ; then, Eq. 16 can be expressed asand the analytical relation between the normalized time τ and the normalized charge X becomes
Here, and are the real roots in the denominators of Eq. 18; meanwhile, the coefficients , , , , , , and are
Furthermore, the equilibrium point of equation system Eq. 15 is met when , that is, ; in other words, ; then, from (15), , having at least one real root corresponding to the value of at the equilibrium point . The singularity point of the system is where the derivative does not exist, that is, ; hence, we get from (15), having at least one real root corresponding to the singular line, for any given . Depending on the initial conditions, Y evolves positively according to Cond-1 and negatively according to Cond-2. Recall that the value of is not known; however, we considered all the possible occurrences as shown in Figure 9. Each trajectory begins with the corresponding value of . Therefore, depending on , we observed different evolution patterns in the phase portraits.
FIGURE 9
The phase portraits show the families of curves for different initial conditions. The results are obtained for and . Note that the memristance is unchanged for and and is, respectively, given by and as depicted by the parallel evolution of the curves outside the interval . Therefore, different possibilities are considered that take into account the case where or one and beyond. The lack of symmetry is highly observable as the curves evolve from left to right for and then from right to left for according to Cond-1 and Cond-2, respectively. Furthermore, the time evolution of cells 1 and 2, respectively, can be obtained from Eqs. 6–9 as follows:where
4 Memristor Fuse
The lack of bilaterality manifested in a bipolar memristor device is challenging in terms of its usage for certain applications, such as communication link in bidirectional applications (). As shown in Figure 6 and Figure 7, using a memristor to link two possible sources of information communicating together bidirectionally is not advisable owing to its resistance dependency on the amount and direction of flowing current. To convert it, a memristor fuse is proposed and then demonstrated in the work of , , and . It is basically formed by connecting two memristors antiserially in order to avoid the lack of bilaterality (). The memristor fuse is reported to be useful in a memristive grid network for CNN neighborhood connection and image processing (, , , , , ). In general (), Figure 10 shows the four possible ways to form series connections of two memristors with respect to their polarities.
FIGURE 10
As shown in Figure 10, cases 1 and 2 refer to a serial connection of two memristors and the memristive effect is retained for these branches. Meanwhile, cases 3 and 4 are identical in structure and refer to antiserial connection of two memristors, thus forming a memristor fuse. The memristive effect for branches in cases 3 and 4 could be suppressed (). However, case 3 is the commonly adopted formation of a memristor fuse (). Note that cases 1 and 2 resemble Figures 4A,B, respectively, with the exception that two memristors are involved.
It is important to note that the resistance of the memristor fuse is the sum of the resistance of each of the individual memristor because the equivalent memristance is additive in a serially connected memristor. In addition, this could be a disadvantage to the desired amount of current and it also affects the dynamic features of the memristor to the extent that the current–voltage graph is merely linear; hence, the formation resembles normal resistor. Therefore, the resistance limits of the memristor fuse must be the same as those of memristor if acting alone.
The pinched hysteresis loop is one of the most distinguished fingerprints of a memristor (, ) and is a reflection of its memory effect. As pointed out in the work of and , without the memory, a memristor is nothing different from a resistor. A verification test is performed to compare the memristor fuse with a standalone memristor, as demonstrated in Figure 11. and are set with their polarity reversed in parallel with a memristor fuse , all connected across the same voltage source . Note that the orientation of and is, respectively, similar to and illustrated in Figures 4A,B. Therefore, for the same resistance limits, the memristance of a memristor fuse is higher than the memristance of a standalone memristor, as can be observed from the respective slopes of Figure 11.
FIGURE 11
Figure 12 shows the schematic of a memristor fuse formed by antiseries connection of two memristors and with the instantaneous dopant width denoted by and , respectively. During positive bias, expands while contracts, and during negative bias, contracts while expands. As tends to D, tends to 0 and the converse gives the opposite. Moreover, and could be represented in normalized forms as and , where and . Then, the drift speeds of the respective dopant are expressed as
FIGURE 12
The same current flows through a series connection of two memristors; hence, is the same for both and . Here, we consider the expression of the memristance given by Eq. 1b rather than the one given in Eq. 10 because it is simpler and already investigated in the work of . From Eqs. 1b, 23, the rates of change of the instantaneous memristance of and are, respectively, obtained to bewhere and . Although the current flowing through them is the same, however, the rate of change of memristance for one differs from the other. Therefore, from 24a and 24b, the rate of change of with respect to that of is given bywhere is called the mismatch factor () describing the increase of with respect to the decrease of and vice versa. Note that , each possibly able to depend on the dimension (D), the mobility of charge carriers, and the value of the lowest resistance () for and , respectively. Thus, the mismatch factor is determined by the mobilities and velocities of charge carriers in both memristors. Given the initial memristance of and as and , respectively, integrating Eq. 25 giveswhere . The net memristance is additive in a series connection of memristors. The instantaneous memristance of the memristor fuse is given by ; thus,
The instantaneous memristance of the memristor fuse depends then on the mismatch factor (ϱ).
Figure 13 shows the comparison of the circuit response for the memristor and memristor fuse using the setup shown in Figure 5. Then, for Cond-1, and , while for Cond-2, and with , , and in each case. Furthermore, Me1 and Me2 represent memristor according to Cond-1 and Cond-2, respectively. Similarly, Mf1 and Mf2 represent the memristor fuse according to Cond-1 and Cond-2, respectively. For each case, the system evolves and eventually stabilizes when .
FIGURE 13
Figure 13A shows the evolution of and for Me1, Me2, Mf1, and Mf2. The results of Me1 and Me2 show a shift difference during the transient state while there is no such shift between the curves of Mf1 and Mf2, showing that the memristor fuse behaves equally in both Cond-1 and Cond-2. Figure 13B shows the currents through the memristor as ie1 and ie2 according to Cond-1 and Cond-2, respectively, and then through the memristor fuse as if1 and if2 according to Cond-1 and Cond-2, respectively. Furthermore, the results show that no current is flowing through the memristor when as similarly observed in the analytical result of Figure 9, that is, when . Figure 13C shows the flowing current through the memristor and the memristor fuse. The results show the differences in the memristor responses according to Cond-1 and Cond-2, but the memristor fuse behaves indifferently in both conditions.
5 Conclusion
We introduced the application of memristor in a nonlinear network, focusing specifically on the behavior of the memristor with respect to the polarity reversal effect of the input signal. Our target is the implementation of memristor-based 2D nonlinear networks for versatile applications, such as signal processing and electronic prosthesis for a synaptic link between real neurons. Here, we investigate the interaction of a bipolar memristor between two RC cells communicating together bidirectionally. In this way, the interaction of the memristor within the network is studied qualitatively and quantitatively. We have shown from the circuit point of view and the analytical solution that the conductivity of the memristor depends on the polarity of the applied input signal, thus affecting the mobility of its charge carriers, this property being due to the intrinsic nature of the device. It is an inevitable nature of a bipolar memristor, irrespective of its device technology. Hence, the memristive effect changes according to the connection mode and the amount of current flowing through it, showing that the memristor is not a bilateral circuit element as verified by our study.
To achieve the memristive effect with symmetry, a memristor fuse is proposed. We present the detail analytical interpretation of the memristor fuse. We also authenticate the memristor fuse prior to apply it in a circuit, and the results show that the memristor fuse behaves like a standalone memristor under high input frequency. Although connecting two memristors antiserially to form a memristor fuse lets the dynamic of the two state variables system become more intricate, as well as the dynamics of the resistance switching (), terminals’ asymmetry is resolved as confirmed by the results shown in Figure 13. The symmetry displayed by the memristor fuse suggests it to be a promising element useful as a memristive grid in neighborhood connections and it could become an important concept for the ongoing study of our memristor-based network.
Statements
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding authors.
Author contributions
All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
References
1
AdhikariS. P.Changju YangC.Hyongsuk KimH.ChuaL. O. (2012). Memristor Bridge Synapse-Based Neural Network and its Learning. IEEE Trans. Neural Netw. Learn. Syst.23, 1426–1435. 10.1109/tnnls.2012.2204770
2
AdhikariS. P.SahM. P.KimH.ChuaL. O. (2013). Three Fingerprints of Memristor. IEEE Trans. Circuits Syst.60, 3008–3021. 10.1109/tcsi.2013.2256171
3
AscoliA.LanzaV.CorintoF.TetzlaffR. (2015). Synchronization Conditions in Simple Memristor Neural Networks. J. Franklin Inst.352, 3196–3220. 10.1016/j.jfranklin.2015.06.003
4
BaoB.YangQ.ZhuD.ZhangY.XuQ.ChenM. (2020). Initial-induced Coexisting and Synchronous Firing Activities in Memristor Synapse-Coupled Morris-Lecar Bi-neuron Network. Nonlinear Dyn.99, 2339–2354. 10.1007/s11071-019-05395-7
5
BiolekZ.BiolekD.BiolkováV. (2012). Computation of the Area of Memristor Pinched Hysteresis Loop. IEEE Trans. Circuits Syst.59, 607–611. 10.1109/tcsii.2012.2208670
6
BiolekZ.BiolekD.BiolkovaV. (2009). Spice Model of Memristor with Nonlinear Dopant Drift. Radioengineering18 (2), 210–214.
7
BorghettiJ.SniderG. S.KuekesP. J.YangJ. J.StewartD. R.WilliamsR. S. (2010). 'Memristive' Switches Enable 'stateful' Logic Operations via Material Implication. Nature464, 873–876. 10.1038/nature08940
8
BoynS.GrollierJ.LecerfG.XuB.LocatelliN.FusilS.et al (2017). Learning through Ferroelectric Domain Dynamics in Solid-State Synapses. Nat. Commun.8, 14736–14737. 10.1038/ncomms14736
9
CampbellK. A. (2017). Self-directed Channel Memristor for High Temperature Operation. Microelectronics J.59, 10–14. 10.1016/j.mejo.2016.11.006
10
ChuM.KimB.ParkS.HwangH.JeonM.LeeB. H.et al (2014). Neuromorphic Hardware System for Visual Pattern Recognition with Memristor Array and Cmos Neuron. IEEE Trans. Ind. Electro.62, 2410–2419. 10.1109/tie.2014.2356439
11
ChuaL. (2015). Everything You Wish to Know about Memristors but Are Afraid to Ask. Radioengineering24, 319–368. 10.13164/re.2015.0319
12
ChuaL. (2014). If It's Pinched It's a Memristor. Semicond. Sci. Technol.29, 104001. 10.1088/0268-1242/29/10/104001
13
ChuaL. (1971). Memristor-the Missing Circuit Element. IEEE Trans. Circuit Theor.18, 507–519. 10.1109/tct.1971.1083337
14
ChuaL. O.Sung Mo KangS. M. (1976). Memristive Devices and Systems. Proc. IEEE64, 209–223. 10.1109/proc.1976.10092
15
ComteJ. C.MarquiéP.BilbaultJ. M. (2001). Contour Detection Based on Nonlinear Discrete Diffusion in a Cellular Nonlinear Network. Int. J. Bifurcation Chaos11, 179–183. 10.1142/s0218127401002134
16
Di VentraM.PershinY. V.ChuaL. O. (2009). Putting Memory into Circuit Elements: Memristors, Memcapacitors, and Meminductors [point of View]. Proc. IEEE97, 1371–1372. 10.1109/jproc.2009.2022882
17
DongaleT. D.DesaiN. D.KhotK. V.VolosC. K.BhosaleP. N.KamatR. K. (2018). An Electronic Synapse Device Based on Tio2 Thin Film Memristor. J. Nanoelectronics Optoelectronics13, 68–75. 10.1166/jno.2018.2297
18
DuanS.HuX.DongZ.WangL.MazumderP. (2015). Memristor-based Cellular Nonlinear/neural Network: Design, Analysis, and Applications. IEEE Trans. Neural Netw. Learn. Syst.26, 1202–1213. 10.1109/TNNLS.2014.2334701
19
DuanS.HuX.WangL.LiC.MazumderP. (2012). Memristor-based Rram with Applications. Sci. China Inf. Sci.55, 1446–1460. 10.1007/s11432-012-4572-0
20
FoudaM. E.KhatibM. A.MosadA. G.RadwanA. G. (2013). Generalized Analysis of Symmetric and Asymmetric Memristive Two-Gate Relaxation Oscillators. IEEE Trans. Circuits Syst.60, 2701–2708. 10.1109/tcsi.2013.2249172
21
GelencserA.ProdromakisT.ToumazouC.RoskaT. (2012). A Biomimetic Model of the Outer Plexiform Layer by Incorporating Memristive Devices. Phys. Rev. E85, 041918. 10.1103/physreve.85.041918
22
HamdiouiS.XieL.Du NguyenH. A.TaouilM.BertelsK.CorporaalH.et al (2015). Memristor Based Computation-In-Memory Architecture for Data-Intensive Applications, 2015 Design, Automation & Test in Europe Conference & Exhibition (DATE); March 2015; Grenoble, France. IEEE, 1718–1725.
23
HuangH.-H.ShihW.-C.LaiC.-H. (2010). Nonpolar Resistive Switching in the Pt/mgo/pt Nonvolatile Memory Device. Appl. Phys. Lett.96, 193505. 10.1063/1.3429024
24
IsahA.NguetchoA. S. T.BinczakS.BilbaultJ. M. (2020a). Memristor Dynamics Involved in Cells Communication for a 2D Non‐linear Network. IET Signal. Process.14, 427–434. 10.1049/iet-spr.2020.0136
25
IsahA.NguetchoA. T.BinczakS.BilbaultJ. (2020b). Dynamics of a Charge-Controlled Memristor in Master–Slave Coupling. Electro. Lett.56, 168. 10.1049/el.2019.3322
26
JiangF.ShiB. E. (2009). The Memristive Grid Outperforms the Resistive Grid for Edge Preserving Smoothing, 2009 European Conference on Circuit Theory and Design (IEEE); Aug. 2009; Antalya, Turkey. 10.1109/ECCTD.2009.5274947IEEE, 181–184.
27
JoS. H.ChangT.EbongI.BhadviyaB. B.MazumderP.LuW. (2010). Nanoscale Memristor Device as Synapse in Neuromorphic Systems. Nano Lett.10, 1297–1301. 10.1021/nl904092h
28
JoglekarY. N.WolfS. J. (2009). The Elusive Memristor: Properties of Basic Electrical Circuits. Eur. J. Phys.30, 661–675. 10.1088/0143-0807/30/4/001
29
KimH.SahM. P.YangC.RoskaT.ChuaL. O. (2011). Memristor Bridge Synapses, Proceedings of the IEEE, 100. IEEE, 2061–2070. 10.1109/JPROC.2011.2166749
30
KrzysteczkoP.ReissG.ThomasA. (2009). Memristive Switching of Mgo Based Magnetic Tunnel Junctions. Appl. Phys. Lett.95, 112508. 10.1063/1.3224193
31
LecerfG.TomasJ.BoynS.GirodS.MangaloreA.GrollierJ.et al (2014). Silicon Neuron Dedicated to Memristive Spiking Neural Networks, 2014 IEEE International Symposium on Circuits and Systems (ISCAS); June 2014; Melbourne, VIC, Australia. 10.1109/ISCAS.2014.6865448IEEE, 1568–1571.
32
LiY.ZhongY.ZhangJ.XuL.WangQ.SunH.et al (2014). Activity-dependent Synaptic Plasticity of a Chalcogenide Electronic Synapse for Neuromorphic Systems. Sci. Rep.4, 4906. 10.1038/srep04906
33
LimC. K. K.GelencserA.ProdromakisT. (2019). Computing Image and Motion with 3-d Memristive Grids. Handbook of Memristor. Networks (Springer), 1177–1210.
34
LinnE.RosezinR.KügelerC.WaserR. (2010). Complementary Resistive Switches for Passive Nanocrossbar Memories. Nat. Mater9, 403–406. 10.1038/nmat2748
35
MaraniR.GelaoG.PerriA. G. (2015). A Review on Memristor Applications. arXiv preprint arXiv:1506.06899
36
MazumderP.KangS. M.WaserR. (2012). Memristors: Devices, Models, and Applications [Scanning the Issue]. Proc. IEEE100, 1911–1919. 10.1109/jproc.2012.2190812
37
MuthuswamyB. (2010). Implementing Memristor Based Chaotic Circuits. Int. J. Bifurcation Chaos20, 1335–1350. 10.1142/s0218127410026514
38
ParisA.TaioliS. (2016). Multiscale Investigation of Oxygen Vacancies in TiO2 Anatase and Their Role in Memristor's Behavior. J. Phys. Chem. C120, 22045–22053. 10.1021/acs.jpcc.6b07196
39
PershinY. V.Di VentraM. (2011). Solving Mazes with Memristors: A Massively Parallel Approach. Phys. Rev. E84, 046703. 10.1103/physreve.84.046703
40
PickettM. D.StrukovD. B.BorghettiJ. L.YangJ. J.SniderG. S.StewartD. R.et al (2009). Switching Dynamics in Titanium Dioxide Memristive Devices. J. Appl. Phys.106, 074508. 10.1063/1.3236506
41
PreziosoM.BayatF. M.HoskinsB.LikharevK.StrukovD. (2016). Self-adaptive Spike-time-dependent Plasticity of Metal-Oxide Memristors. Scientific Rep.6, 1–6. 10.1038/srep21331
42
ProdromakisT.ToumazouC. (2010). A Review on Memristive Devices and Applications, 2010 17th IEEE International Conference on Electronics, Circuits and Systems; Dec. 2010; Athens, Greece. IEEE, 934–937. 10.1109/ICECS.2010.5724666
43
SaïghiS.MayrC. G.Serrano-GotarredonaT.SchmidtH.LecerfG.TomasJ.et al (2015). Plasticity in Memristive Devices for Spiking Neural Networks. Front. Neurosci.9, 51. 10.3389/fnins.2015.00051
44
Sarmiento-ReyesA.Rodríguez-VelásquezY. (2018). Maze-solving with a Memristive Grid of Charge-Controlled Memristors (LASCAS), 2018 IEEE 9th Latin American Symposium on Circuits & Systems; Feb. 2018; Puerto Vallarta, Mexico. (IEEE), 1–4. 10.1109/LASCAS.2018.8399973
45
SerbA.KhiatA.ProdromakisT. (2016). Practical Demonstration of a Memristive Fuse. arXiv preprint arXiv:1609.02410
46
ShinS.KimK.KangS.-M. (2010). Memristor Applications for Programmable Analog IcsIEEE Transactions on Nanotechnology, 10. (IEEE), 266–274. 10.1109/TNANO.2009.2038610
47
SimmonsJ. G. (1971). Conduction in Thin Dielectric Films. J. Phys. D: Appl. Phys.4, 613–657. 10.1088/0022-3727/4/5/202
48
SimmonsJ. G. (1963a). Electric Tunnel Effect between Dissimilar Electrodes Separated by a Thin Insulating Film. J. Appl. Phys.34, 2581–2590. 10.1063/1.1729774
49
SimmonsJ. G. (1963b). Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film. J. Appl. Phys.34, 1793–1803. 10.1063/1.1702682
50
Stanley WilliamsR. (2013). How We Found the Missing Memristor, Chaos, CNN, Memristors and Beyond: A Festschrift for Leon Chua With DVD-ROM, composed by Eleonora Bilotta (World Scientific). (IEEE), 483–489. 10.1109/MSPEC.2008.4687366
51
StrachanJ. P.StrukovD. B.BorghettiJ.Joshua YangJ.Medeiros-RibeiroG.Stanley WilliamsR. (2011). The Switching Location of a Bipolar Memristor: Chemical, thermal and Structural Mapping. Nanotechnology22, 254015. 10.1088/0957-4484/22/25/254015
52
StrukovD. B.SniderG. S.StewartD. R.WilliamsR. S. (2008). The Missing Memristor Found. nature453, 80–83. 10.1038/nature06932
53
TeixeiraJ. M.VenturaJ.FermentoR.AraujoJ. P.SousaJ. B.WisniowskiP.et al (2009). Electroforming, Magnetic and Resistive Switching in Mgo-Based Tunnel Junctions. J. Phys. D: Appl. Phys.42, 105407. 10.1088/0022-3727/42/10/105407
54
ThomasA. (2013). Memristor-based Neural Networks. J. Phys. D: Appl. Phys.46, 093001. 10.1088/0022-3727/46/9/093001
55
VolosC. K.KyprianidisI.StouboulosI.Tlelo-CuautleE.VaidyanathanS. (2015). Memristor: A New Concept in Synchronization of Coupled Neuromorphic Circuits. J. Eng. Sci. Techn. Rev.8. 10.25103/jestr.082.21
56
WangC.HeW.TongY.ZhaoR. (2016). Investigation and Manipulation of Different Analog Behaviors of Memristor as Electronic Synapse for Neuromorphic Applications. Sci. Rep.6, 22970. 10.1038/srep22970
57
WangZ.JoshiS.Savel’evS. E.JiangH.MidyaR.LinP.et al (2017). Memristors with Diffusive Dynamics as Synaptic Emulators for Neuromorphic Computing. Nat. Mater16, 101–108. 10.1038/nmat4756
58
XuF.ZhangJ.FangT.HuangS.WangM. (2018). Synchronous Dynamics in Neural System Coupled with Memristive Synapse. Nonlinear Dyn.92, 1395–1402. 10.1007/s11071-018-4134-0
59
Xu Ya-MingY.-M.Wang Li-DanL.-D.Duan Shu-KaiS.-K. (2016). A Memristor-Based Chaotic System and its Field Programmable Gate Array Implementation. wlxb65, 120503. 10.7498/aps.65.120503
60
YakopcicC.HasanR.TahaT. M. (2018). Flexible Memristor Based Neuromorphic System for Implementing Multi-Layer Neural Network Algorithms. Int. J. Parallel, Emergent Distributed Syst.33, 408–429. 10.1080/17445760.2017.1321761
61
YangC.KimH. (2016). Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing. Sensors16, 1320. 10.3390/s16081320
62
YangJ. J.PickettM. D.LiX.OhlbergD. A. A.StewartD. R.WilliamsR. S. (2008). Memristive Switching Mechanism for Metal/oxide/metal Nanodevices. Nat. Nanotech3, 429–433. 10.1038/nnano.2008.160
63
YildirimM.BabacanY.KacarF. (2018). Memristive Retinomorphic Grid Architecture Removing Noise and Preserving Edge. AEU - Int. J. Electro. Commun.97, 38–44. 10.1016/j.aeue.2018.10.001
64
YinL.ChengR.WangZ.WangF.SendekuM. G.WenY.et al (2020). Two-dimensional Unipolar Memristors with Logic and Memory Functions. Nano Lett.20, 4144–4152. 10.1021/acs.nanolett.0c00002
65
YoshidaC.KurasawaM.LeeY. M.AokiM.SugiyamaY. (2008). Unipolar Resistive Switching in CoFeB∕MgO∕CoFeB Magnetic Tunnel junction. Appl. Phys. Lett.92, 113508. 10.1063/1.2898514
66
ZhangJ.LiaoX. (2017). Synchronization and Chaos in Coupled Memristor-Based Fitzhugh-Nagumo Circuits with Memristor Synapse. AEU - Int. J. Electro. Commun.75, 82–90. 10.1016/j.aeue.2017.03.003
Summary
Keywords
cellular nonlinear networks, memristor, bilateral, asymmetry, charged cells, memristor fuse
Citation
Isah A, Tchakoutio Nguetcho AS, Binczak S and Bilbault JM (2021) Polarity Reversal Effect of a Memristor From the Circuit Point of View and Insights Into the Memristor Fuse. Front. Comms. Net 2:647528. doi: 10.3389/frcmn.2021.647528
Received
06 January 2021
Accepted
15 June 2021
Published
07 July 2021
Volume
2 - 2021
Edited by
Ilangko Balasingham, Norwegian University of Science and Technology, Norway
Reviewed by
Valentina Lanza, University of Le Havre, France
Zhongrui Wang, The University of Hong Kong, China
Updates
Copyright
© 2021 Isah, Tchakoutio Nguetcho, Binczak and Bilbault.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Aliyu Isah, aliyu_isah@etu.u-bourgogne.fr, aliyuisahbabanta@gmail.com; J.M. Bilbault, jean-marie.bilbault@u-bourgogne.fr.
This article was submitted to Non-Conventional Communications and Networks, a section of the journal Frontiers in Communications and Networks
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