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Chimera States in Complex Networks

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Dynamics of complex networks is a central issue in nonlinear science with applications to different fields ranging from natural to technological and socio-economic systems. The interplay of nonlinear dynamics, network topology, naturally arising delays, and random fluctuations results in a plethora of ...

Dynamics of complex networks is a central issue in nonlinear science with applications to different fields ranging from natural to technological and socio-economic systems. The interplay of nonlinear dynamics, network topology, naturally arising delays, and random fluctuations results in a plethora of spatio-temporal synchronization patterns.

Chimera states in dynamical networks consist of coexisting domains of spatially coherent (synchronized) and incoherent (desynchronized) behavior. They are a manifestation of spontaneous symmetry-breaking in systems of identical oscillators, and occur in a variety of physical, chemical, biological, neuronal, ecological, technological, or socio-economic systems.

In this Research Topics, we focus on recent developments with future promising perspectives, for instance, chimera patterns in small networks, adaptive networks, complex coupling topologies like modular, hierarchical, or multilayer connectivity, coupled phase and amplitude dynamics, multiple delayed-feedback chimeras, coherence resonance chimeras, and control methods for stabilizing chimera states.

In particular, multilayer networks where the nodes are distributed in different layers offer better representation of the topology and dynamics of real-world systems in comparison with one-layer structures. One of the most promising applications of the multilayer approach is the study of the brain, where the neurons can form different layers depending on their connectivity through chemical or electrical synapses, or technological interdependent systems, i.e., those systems in which the correct functioning of one of them strongly depends on the status of the others. For instance, multilayer networks with interconnected layers naturally occur in transportation systems and electrical power grids. The intriguing dynamics of multiplex networks includes relay synchronization and partial synchronization patterns like chimera states.


Keywords: Nonlinear dynamics, oscillator networks, synchronization, chimera states, multilayer networks


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