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

TL;DR

This paper investigates the emergence and properties of chimera states in networks of coupled oscillators inspired by population dynamics, revealing how network topology and parameters influence their multiplicity and motion.

Contribution

It introduces a numerical study of chimera states in a three-species population model with hierarchical and nonlocal coupling, highlighting new dynamical behaviors and topological effects.

Findings

Chimera states coexist with synchronization and desynchronization in the model.

Multiplicity of chimera states depends on system and coupling parameters.

Hierarchical coupling induces traveling multichimera states.

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.