Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

Abstract

We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera states in this spiking regime as a coexistence of coherence (synchronization) and incoherence (desynchronization) in a one-dimensional ring with nonlocal coupling, and demonstrate that their multiplicity depends both on the system and the coupling parameters. We also show that hierarchical (fractal) coupling topologies induce traveling multichimera states. The speed of motion of the coherent and incoherent parts along the ring is computed through the Fourier spectra of the corresponding dynamics.

Multifaceted Dynamics of Janus Oscillator Networks

“…Another example is the breathing chimeras [22] in the solvable two-population model. Traveling chimera states have also been identified in phase and limit cycle oscillators with various nonlocal coupling schemes [48][49][50]. The local coupling scheme in the ring of Janus oscillators constitutes a particularly simple model in which to study traveling chimera states.…”

Mechanisms of appearance of amplitude and phase chimera states in ensembles of nonlocally coupled chaotic systems

“…The chimera states were firstly described in a system of coupled phase oscillators [2]. Since then, they were also found in a wide range of different models including both discrete-time maps and continuous-time (differential) systems with regular and chaotic dynamics [8,9,10,11,12,13,14,15]. The existence of chimera states was repeatedly confirmed not only numerically but also experimentally [16,17,18,19].…”

Relay synchronization in multiplex networks of discrete maps

“…Chimeras have been successfully verified in experiments, including optical [41], chemical [42,43], mechanical [44,45], electronic and optoelectronic [46,47] and electrochemical oscillator networks [48][49][50]. Further, the robustness of chimera states has been demonstrated in networks of inhomogeneous oscillators [51], or with irregular topologies [9,34,39,[52][53][54][55][56][57][58][59].…”