<?xml version="1.0" encoding="utf-8"?>
    <rss version="2.0">
      <channel xmlns:content="http://purl.org/rss/1.0/modules/content/">
        <title>Frontiers in Applied Mathematics and Statistics | Dynamical Systems section | New and Recent Articles</title>
        <link>https://www.frontiersin.org/journals/applied-mathematics-and-statistics/sections/dynamical-systems</link>
        <description>RSS Feed for Dynamical Systems section in the Frontiers in Applied Mathematics and Statistics journal | New and Recent Articles</description>
        <language>en-us</language>
        <generator>Frontiers Feed Generator,version:1</generator>
        <pubDate>2026-05-14T07:16:08.554+00:00</pubDate>
        <ttl>60</ttl>
        <item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2026.1826475</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2026.1826475</link>
        <title><![CDATA[Generation of new batik floral patterns via chaotic modulation and Julia-Mandelbrot fractal transformations]]></title>
        <pubdate>2026-05-11T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Michael Kopp</author><author>Inna Samuilik</author>
        <description><![CDATA[This paper presents a novel hierarchical approach for generating complex floral patterns through sequential application of chaotic modulation and fractal transformations. Classical geometric floral patterns are first subjected to binary chaotic modulation using signals extracted from a four-dimensional memristor-based hyperchaotic system, introducing controlled irregularity into regular structures. Subsequently, Julia and Mandelbrot set-based fractal transformations embed hierarchical self-similarity within these chaotically modulated configurations. The choice of the hyperchaotic system is motivated by its minimal complexity enabling practical analog and digital implementation, hyperchaotic dynamics providing rich modulation signals, and capability to generate multi-scroll attractors. Analysis demonstrates that global geometric order coexists with local fractal complexity in the resulting patterns, with topological features and symmetries partially preserved throughout the transformation cascade. This synergistic synthesis of chaotic dynamics and fractal geometry opens new possibilities for generating patterns with tunable visual and topological characteristics applicable to digital art and textile design.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2026.1790416</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2026.1790416</link>
        <title><![CDATA[Modeling cross-market capital flows using fractional competition dynamics]]></title>
        <pubdate>2026-04-16T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Sherif Abdul Ganiyu</author><author>Mercy Ngungu</author><author>Rebecca Bottey</author><author>Susana Danso Mensah</author>
        <description><![CDATA[IntroductionInteractions between the stock market and the rapidly expanding cryptocurrency market have become an important feature of modern financial systems. Compared with traditional equity markets, cryptocurrency markets are generally more volatile and more sensitive to investor sentiment, speculative behavior, and technological change. Classical integer-order models may not adequately capture the nonlinear interactions, delayed responses, and memory effects that characterize such cross-market capital dynamics.MethodsThis study develops a fractional-order Lotka-Volterra competition model to describe the dynamic competition between stock and cryptocurrency markets. The model employs Caputo fractional derivatives to incorporate memory effects and persistent shocks, and includes migration terms to represent capital reallocation between the two markets. The resulting system is investigated numerically using the fractional Adams-Bashforth-Moulton predictor-corrector scheme.ResultsNumerical simulations show that the fractional-order parameter has a substantial effect on market behavior. Lower fractional orders produce stronger memory effects, slower convergence to equilibrium, and smoother long-term transitions, whereas higher orders recover behavior closer to the classical integer-order case. The simulations further indicate that changes in competition coefficients and capital migration rates strongly affect long-term market dominance, coexistence, and equilibrium levels.DiscussionThe proposed fractional competition framework provides a more flexible and realistic description of stock-cryptocurrency interactions than classical models. By accounting for memory-driven dynamics, it offers useful insight into long-term capital allocation, market coexistence, and the possible influence of regulatory conditions and investor sentiment. These findings suggest that fractional-order modeling can serve as a valuable tool for studying evolving financial markets and cross-market capital flows.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2026.1807939</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2026.1807939</link>
        <title><![CDATA[LaSIPDE: Latent-Space Identification of Partial Differential Equations from indirect, high-dimensional measurements]]></title>
        <pubdate>2026-04-14T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Imane Koulali</author><author>Erhan Turan</author><author>M. Taner Eskil</author>
        <description><![CDATA[Discovering governing equations from data is a central challenge in scientific machine learning, particularly when observations are high-dimensional and the underlying state variables are not directly accessible. In this work, we introduce a framework for data-driven discovery of partial differential equations (PDEs) from indirect high-dimensional observations. The proposed approach combines nonlinear representation learning through an autoencoder with sparse identification of governing equations in the latent space, enabling simultaneous model reduction and PDE discovery while preserving spatial structure. Unlike existing methods that either operate on observable variables or discover latent ordinary differential equations, our framework identifies PDEs directly in the learned latent coordinates. We validate the approach on high-dimensional observations generated from Burgers and Korteweg–de Vries (KdV) systems, where the true state variables are intentionally hidden. In both cases, the method successfully recovers the correct dynamical operators, including diffusion, nonlinear advection, and dispersive terms. Although the recovered coefficients differ due to latent coordinate transformations, we show both theoretically and empirically that the discovered equations are dynamically equivalent to the ground-truth systems up to an affine transformation. These results demonstrate that governing PDEs can be recovered from indirect, high-dimensional data without access to the physical state variables, providing a foundation for interpretable model discovery in realistic measurement settings.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2026.1694271</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2026.1694271</link>
        <title><![CDATA[Optimization of biodiesel synthesis using ultrasound and mechanical stirring methods: a comparative study]]></title>
        <pubdate>2026-02-24T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Sk Mosaraf Ahammed</author><author>Amit Kumar Roy</author><author>Xue-Zhi Li</author><author>Fahad Al Basir</author><author>Priti Kumar Roy</author>
        <description><![CDATA[Mechanical stirring (MS) and ultrasound (US) frequency are two key factors commonly used to reduce mass-transfer resistance during the reaction between methanol (MeOH) and triglycerides (TG), facilitating the efficient production of biodiesel (BD) from various feedstocks such as rapeseed oil and Jatropha curcas oil. In this study, a comparative model analysis has been conducted to evaluate the performance efficacy of optimum mechanical stirring (MS) and optimum ultrasound (US) frequency using rapeseed oil biodiesel production. Sensitivity and uncertainty analyses have been conducted using Latin hypercube sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs) to identify the key kinetic and transport parameters influencing biodiesel yield. An optimal control framework has also been applied to regulate MS speed and US frequency over time to overcome initial mass-transfer resistance between oil and methanol. The influence of mixing intensity on biodiesel conversion has been examined at different temperatures and MeOH:oil molar ratios using mass-transfer correlations for both MS and US frequency. Numerical results show that, at a MeOH:TG molar ratio of 6:1 and temperature of 50 °C, optimal US frequency achieves a maximum biodiesel conversion of 97.67% within 40 min, whereas optimal MS attains 95.32% conversion after 60 min. The results further indicate that ultrasound provides faster mass-transfer enhancement and a superior production profile compared to mechanical stirring. This study addresses two key questions: whether rapeseed oil is a suitable feedstock for biodiesel production, and which mixing strategy, MS or US frequency, more effectively minimizes the mass-transfer resistance over time.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1687991</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1687991</link>
        <title><![CDATA[Dynamical behavior of a stochastic SEIQRV infectious model with an Ornstein-Uhlenbeck process and general incidence]]></title>
        <pubdate>2025-10-14T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Wen-He Li</author><author>Ke-Jia Wu</author>
        <description><![CDATA[Considering the influence of quarantine and vaccination factors, this study examines an SEIQRV infectious disease model that incorporates an Ornstein-Uhlenbeck process and a general incidence function. By accounting for disease-induced mortality rates among infected individuals, the article establishes the existence and uniqueness of a global solution for any arbitrary positive initial value. An adequate condition for disease extinction is also provided. Simultaneously, by reconstructing a sequence of random Lyapunov functions, we demonstrate the existence of a unique stationary distribution indicating that the disease persists over a period of time in a biological sense. Based on these findings, the precise expression for the probability density function of the stochastic model near the quasi-equilibrium state is derived. Finally, the theoretical results are verified through a series of numerical simulations.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1624159</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1624159</link>
        <title><![CDATA[Assessing organizational efficiency in AI-based GHRM using fuzzy SWARA and MOORA mathematical modeling]]></title>
        <pubdate>2025-09-10T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Nitendra Kumar</author><author>Reema Agarwal</author><author>Neeti Sharma</author><author>Khursheed Alam</author><author>Ankur Agrawal</author>
        <description><![CDATA[IntroductionThis study explores the shift in Green Human Resource Management (GHRM) through Artificial Intelligence (AI) adoption by looking at sustainability-driven practices and assessing how they affect organizational eco-efficiency in six different companies in order to run them efficiently and effectively. This research paper evaluates the efficiency of six companies in implementing AI-GHRM practices using ten key criteria.MethodsTo ensure a robust and structured decision-making process under conditions of uncertainty, two prominent fuzzy Multi-Criteria Decision-Making (MCDM) mathematical modeling—Fuzzy Step-wise Weight Assessment Ratio Analysis (F-SWARA) and Fuzzy Multi-Objective Optimization on the basis of Ratio Analysis (F-MOORA) are applied in a fuzzy environment. Applying linguistic factors to account for the subjectivity and ambiguity of human evaluations, the SWARA approach is used to calculate the relative relevance of the ten AI-GHRM criteria based on buying managers’ judgments expressed in terms of triangular fuzzy numbers. These criteria weights are then used in the fuzzy MOORA mathematical modeling method to rank the companies in terms of their overall efficiency in AI-GHRM adoption.Results and discussionsThe results provide a comprehensive ranking of the companies, highlighting best practices and offering insights into strategic areas for improvement. This paper offers a unique hybrid paradigm for performance evaluation under fuzzy settings, advancing both academic and practical knowledge of sustainable HRM integration with AI technology. The findings of the paper are that the fifth company was placed first.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1625802</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1625802</link>
        <title><![CDATA[Can associative memory be modeled by quantum information?]]></title>
        <pubdate>2025-09-03T00:00:00Z</pubdate>
        <category>Brief Research Report</category>
        <author>Michael Siomau</author>
        <description><![CDATA[Associative memory is the ability to reveal similarities between unrelated items. Models of associative memory typically rely on significant assumptions about information encoding procedure, structure of underlying complex network, computational power of nodes, and communication capacity of links. Keeping assumptions plausible and at minimum, the search for association can be done on a network enhanced with quantum information processing exploiting non-locality and quantum state comparison.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1642676</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1642676</link>
        <title><![CDATA[Epidemic dynamics in the spatio-temporal predator-prey model]]></title>
        <pubdate>2025-08-22T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Hyangim Ji</author><author>Maria Vasilyeva</author><author>Nana Adjoah Mbroh</author><author>Alexey Sadovski</author>
        <description><![CDATA[In this work, we develop a novel mathematical model to simulate the spatio-temporal dynamics of epidemics in a predator–prey system. The model integrates the classical Lotka–Volterra predator–prey framework with a Susceptible–Infected–Susceptible disease model and explicitly incorporates diffusion terms to capture spatial movement. This unified approach allows us to simultaneously analyze susceptible and infected prey and predator populations, and account for both ecological and spatial interactions. An extension beyond traditional models that often treat these processes separately. The model consists of four partial differential equations and includes key ecological factors such as growth and mortality rates, predation, reproduction, and carrying capacity. Through extensive numerical simulations across a wide range of ecological and epidemiological parameters, we systematically investigate how disease transmission and spatial diffusion shape population dynamics. The results reveal that spatial movement plays a critical role in determining species distribution and infection persistence, highlighting the complex interplay between disease spread and ecosystem stability.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1521177</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1521177</link>
        <title><![CDATA[Improving immunization initiatives in the dynamics of a typhoid fever transmission model with environmental bacteria concentration]]></title>
        <pubdate>2025-07-29T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Haileyesus Tessema</author><author>Yimer Zemenu</author><author>Endlkachew Bizualem</author><author>Getachew Teshome</author>
        <description><![CDATA[Typhoid fever is a potentially fatal disease and endemic to most parts of the world. It is a serious worldwide health issue, especially in developing countries, and is typically spread via contaminated food, water, or drink. This work introduced an SIVR-B model to explore and predict the dynamics of typhoid disease in a community. The effective reproduction number (REff) of the model is calculated by manipulating the next-generation method. Then, after we computed the Typhoid fever-free equilibrium and the typhoid fever persistence equilibrium points, we demonstrated the global asymptotic stability of the equilibria. The bifurcation analysis demonstrated that the formulated typhoid model exhibits a forward bifurcation at REff = 1. Further, the sensitivity of parameters is performed using normalized forward sensitivity analysis and demonstrated using numerical simulation. The work demonstrated that higher typhoid vaccination rates have a pronounced effect on lowering disease transmission. From the results, we recommended policymakers and government stakeholders should enhance immunization efforts to effectively address the dynamics of typhoid fever transmission. In addition to improving vaccination efficacy, the research work recommends reducing poor drainage systems and improving water quality to reduce the infection number.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1608177</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1608177</link>
        <title><![CDATA[Hyers-Ulam, Rassias, and Mittag-Leffler stability for quantum difference equations in β-calculus]]></title>
        <pubdate>2025-05-22T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Dalal Marzouq AlMutairi</author><author>Chokri Chniti</author><author>Saleh M. Alzahrani</author>
        <description><![CDATA[This paper investigates first-order nonlinear quantum difference equations governed by a general β-difference operator, encompassing the Jackson q-difference and Hahn difference operators as special cases. We establish sufficient conditions for the existence and uniqueness of solutions using fixed-point theory and examine their solvability under specific assumptions to ensure well-posedness. Particular attention is given to various notions of stability, including Hyers-Ulam, Hyers-Ulam-Rassias, and Mittag-Leffler type stability. Under suitable Lipschitz conditions, we derive explicit error bounds characterizing each type of stability, with Mittag-Leffler stability demonstrated to be of exponential order α. Several illustrative examples are included to validate the theoretical findings within the framework of quantum calculus and discrete dynamical systems.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1544002</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1544002</link>
        <title><![CDATA[Analysis of new mathematical model for rabies through wavelet method]]></title>
        <pubdate>2025-04-23T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>R. Yeshwanth</author><author>S. Kumbinarasaiah</author><author>Sharanjeet Dhawan</author>
        <description><![CDATA[Rabies is a fatal zoonotic disease caused by a virus, primarily spread through bites or saliva. Dogs are the main source of human infections worldwide. This article introduces a new mathematical model using fractional differential equations to analyze rabies transmission dynamics. The model consists of four compartments: susceptible and infected populations of both humans and animals, forming a system of fractional differential equations (SOFDEs). The modified Hermite wavelet collocation method (HWCM) is used to solve these equations by converting them into a non-linear algebraic system. Newton-Raphson's approach determines the unknown Hermite coefficients, and the results are compared with ND Solver and RK4 methods. Visual and numerical analysis confirms the proposed method's superior accuracy and effectiveness.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1517447</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1517447</link>
        <title><![CDATA[Implementation of the banking dynamics model using a system of deterministic differential equations]]></title>
        <pubdate>2025-04-04T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Aloysius Vincent</author><author>Novriana Sumarti</author>
        <description><![CDATA[IntroductionThis study discusses modeling the interaction among components of a bank’s balance sheet, consisting of deposit, loan, and equity, as a useful tool for analyzing risk conditions arising from factors such as non-performing loans (NPSLs) and deposit withdrawals.MethodsThe model utilizes a deterministic differential equation system based on a modified logistic growth model.ResultsWhen applied to data of selected banks in Indonesia under certain assumptions, the model effectively describes the growth of their balance sheets.DiscussionOur findings indicate that banks with higher core capital do not necessarily exhibit more stable equilibrium than those with lower core capital. Additionally, the equity equilibrium does not show a consistent pattern among banks with varying levels of core capital.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1530570</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1530570</link>
        <title><![CDATA[Detection of neonatal asphyxia by analyzing the complexity of electroencephalography data]]></title>
        <pubdate>2025-03-19T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Sou Nobukawa</author><author> Kurnianingsih</author><author>Isshu Wakita</author><author>Ayumu Ueno</author><author>Melyana Nurul Widyawati</author><author>Cipta Pramana</author><author>Nurseno Bayu Aji</author><author>Afandi Nur Aziz Thohari</author><author>Dwiana Hendrawati</author><author>Eri Sato-Shimokawara</author><author>Naoyuki Kubota</author>
        <description><![CDATA[IntroductionIn neonates, the early detection of asphyxia improves survival rates and prevents long-term complications. In neonatal care, physiological signals, including heart rate and oxygen saturation, are routinely monitored. However, neonates with neurological conditions such as hypoxic-ischemic encephalopathy (HIE) require direct neural monitoring. Electroencephalography (EEG) is a non-invasive method for assessing neural activity and therefore can effectively detect early signs of asphyxia. Although studies on HIE have utilized clinical-grade EEG systems, the real-world application of wearable EEG devices in broader neonatal care remains underexplored. In this study, we aimed to investigate the effectiveness of wearable EEG devices in detecting asphyxia without restricting its progression to hypoxic-ischemic encephalopathy (HIE).MethodsWe used Fuzzy Entropy (FuzzyEn) to perform power spectral and complexity analyses on EEG signal data healthy neonates and those with asphyxia.ResultsWe found that both delta band power and EEG signal complexity decrease in neonates with asphyxia, which is consistent with those of studies on HIE. Furthermore, FuzzyEn in combination with absolute power measurements captured complementary information that led to improved detection accuracy and enhanced identification performance.DiscussionWearable EEG devices are scalable and accessible for use in resource-constrained environments (such as rural and developing regions) and can be integrated into Internet of Things (IoT) systems. Our findings highlight the potential of wearable EEG devices in early detection of asphyxia, which may contribute to a more effective neonatal care and improved survival outcomes.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1584781</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1584781</link>
        <title><![CDATA[Editorial: Approximation methods and analytical modeling using partial differential equations]]></title>
        <pubdate>2025-03-18T00:00:00Z</pubdate>
        <category>Editorial</category>
        <author>Kateryna Buryachenko</author><author>Marina Chugunova</author><author>Yurii Kolomoitsev</author>
        <description></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2025.1410533</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2025.1410533</link>
        <title><![CDATA[Two-warehouse deterministic inventory model of expiry date known deteriorating items with just-in-time purchases for slotted backlogs]]></title>
        <pubdate>2025-02-05T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>R. Thilagavathi</author><author>J. Viswanath</author><author>Miroslav Mahdal</author><author>Jayavelu Udaya Prakash</author><author>Sachin Salunkhe</author>
        <description><![CDATA[IntroductionA two-warehouse deterministic inventory system for purchases of short-expiry items with low purchasing costs is modelled. The total cost of the replenishment cycle is arrived at by implementing multiple just-in-time (JIT) purchases for the slotted backlogged customers. It avoids the loss of impatient customers who are virtually waiting for a long time.MethodsThe inventory system consists of an own warehouse (OW) with finite capacity and an integral rental warehouse (RW) with unlimited capacity. Handlingand selling items with short expiry is a challenging task in revenue generation in commercial inventory management. Two categories of identical items are purchased: Category 1 consists of items whose expiry date falls within the replenishment cycle period, while Category 2 includes items with longer expiry dates. Unlike the traditional assumption in the literature, the items in Category 1 are purchased for a low price and stored in RW. Items in Category 2 are stored in OW. Due to short expiry of items, demands are first satisfied from the RW. The items in the RW are emptied before the expiry date of the items, due to expiry date-dependent deterioration and constant demand. At the same time, the items in the OW are decreasing due to exponential demand and constant deterioration. All customers are backlogged during the stock-out period and slotted into three intervals. The finite number of JIT purchases is employed to satisfy the backlogged slotted demands that occur before the last slot.Results and DiscussionWe optimize the total cost of the replenishment cycle, RW utility, and total items purchased. The model is illustrated with an appropriate numerical example, and extensive sensitivity analysis is conducted on the system’s performance.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2024.1502500</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2024.1502500</link>
        <title><![CDATA[Analysis of school bullying menace incorporating family education: a mathematical modeling approach]]></title>
        <pubdate>2025-01-09T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Adejimi Adeniji</author><author>Emmanuel Addai</author><author>Shatalov Michael</author><author>Kekana Malesela</author><author>Joshua Kiddy K. Asamoah</author><author>Kayode Oshinubi</author>
        <description><![CDATA[School bullying is a severe social problem that has an unfavorable impact on students development and behavior. Based on family education and students memory of having been bullied or witnessed bullying, this work established a mathematical model for analyzing school bullying dynamics. By employing the Caputo fractional derivative, the model incorporates students' memory in the interactional patterns of bullying, which provides for improved emulation of the impacts of previous episodes on future behaviors. An Adams-Bashforth method numerical scheme is presented, offering a robust approach for scenario simulations under the Caputo fractional operator. Scenario simulations shows the impact of family education on the prevalence and dynamics of school bullying. It is noticed that the behavior of students who lack and with family education and not involving bullying under different values of fractional order. The trajectory changes with the fractional order, suggesting that the system's sensitivity to initial conditions or recent changes decreases as fractional order reduce from the normal dynamics (integer order). Essentially, a lower fractional order makes the system less reactive to short-term fluctuations and more stable.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2024.1466569</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2024.1466569</link>
        <title><![CDATA[Some class of nonlinear partial differential equations in the ring of copolynomials over a commutative ring]]></title>
        <pubdate>2024-11-22T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Sergiy L. Gefter</author><author>Aleksey L. Piven'</author>
        <description><![CDATA[We study the copolynomials, i.e., K-linear mappings from the ring of polynomials K[x] into the commutative ring K. With the help of the Cauchy–Stieltjes transform of a copolynomial, we introduce and examine a multiplication of copolynomials. We investigate the Cauchy problem related to the nonlinear partial differential equation ∂u∂t=aum0(∂u∂x)m1(∂2u∂x2)m2(∂3u∂x3)m3,   m0,m1,m2,m3∈ℕ0,   ∑j=03mj>0,   a∈K in the ring of copolynomials. To find a solution, we use the series of powers of the δ-function. As examples, we consider the Cauchy problem with the Euler–Hopf equation ∂u∂t+u∂u∂x=0, for a Hamilton–Jacobi type equation ∂u∂t=(∂u∂x)2, and for the Harry Dym equation ∂u∂t=u3∂3u∂x3.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2024.1471447</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2024.1471447</link>
        <title><![CDATA[Corrigendum: A scalar Poincaré map for anti-phase bursting in coupled inhibitory neurons with synaptic depression]]></title>
        <pubdate>2024-11-06T00:00:00Z</pubdate>
        <category>Correction</category>
        <author>Mark Olenik</author><author>Conor Houghton</author>
        <description></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2024.1456635</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2024.1456635</link>
        <title><![CDATA[Disentangling dynamic and stochastic modes in multivariate time series]]></title>
        <pubdate>2024-10-22T00:00:00Z</pubdate>
        <category>Methods</category>
        <author>Christian Uhl</author><author>Annika Stiehl</author><author>Nicolas Weeger</author><author>Markus Schlarb</author><author>Knut Hüper</author>
        <description><![CDATA[A signal decomposition is presented that disentangles the deterministic and stochastic components of a multivariate time series. The dynamical component analysis (DyCA) algorithm is based on the assumption that an unknown set of ordinary differential equations (ODEs) describes the dynamics of the deterministic part of the signal. The algorithm is thoroughly derived and accompanied by a link to the GitHub repository containing the algorithm. The method was applied to both simulated and real-world data sets and compared to the results of principal component analysis (PCA), independent component analysis (ICA), and dynamic mode decomposition (DMD). The results demonstrate that DyCA is capable of separating the deterministic and stochastic components of the signal. Furthermore, the algorithm is able to estimate the number of linear and non-linear differential equations and to extract the corresponding amplitudes. The results demonstrate that DyCA is an effective tool for signal decomposition and dimension reduction of multivariate time series. In this regard, DyCA outperforms PCA and ICA and is on par or slightly superior to the DMD algorithm in terms of performance.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fams.2024.1396650</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fams.2024.1396650</link>
        <title><![CDATA[Fractional-order analysis of temperature- and rainfall-dependent mathematical model for malaria transmission dynamics]]></title>
        <pubdate>2024-10-09T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Ademe Kebede Gizaw</author><author>Chernet Tuge Deressa</author>
        <description><![CDATA[Malaria remains a substantial public health challenge and economic burden globally. Currently, malaria has been declared as endemic in 85 countries. In this study, we developed and analyzed a fractional-order mathematical model for malaria transmission dynamics that incorporates variability of temperature and rainfall using Caputo-type AB operators. The existence and uniqueness of the model's solutions were established using the Banach fixed-point theorem. The model system's equilibria (both disease-free and endemic) were identified, and lemmas and theorems were developed to prove their stability. Furthermore, we used different temperature ranges and rainfall data, validating them against existing literature. Numerical simulations using the Toufik-Atangana schemes with various fractional-order alpha values revealed that as the value of alpha approaches 1, the behavior of the fractional-order model converges to that of the classical model. The numerical results are promising and are expected to be valuable for future research related to fractional-order models.]]></description>
      </item>
      </channel>
    </rss>