Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities.
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 on both 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.
Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15310 Athens, Greece.|Crete Center for Quantum Complexity and Nanotechnology, Department of Physics, University of Crete, 71003 Heraklion, Greece.
Johanne
J
Hizanidis
Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15310 Athens, Greece.
Evangelia
E
Panagakou
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
Iryna
I
Omelchenko
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
Eckehard
E
Schöll
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.|Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany.
Philipp
P
Hövel
Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15310 Athens, Greece.
Astero
A
Provata
D008962:Models, Theoretical