Seminar: Applications of Complex Networks - Winter Term 2014/15

Location: EW 731

Time: Tuesday, 16.12.2014, 12:15

Chimera states in the Lattice Limit Cycle model with piecewise and hierarchical network connectivity

Astero Provata, Johanne Hizanidis

The Lattice Limit Cycle (LLC) model is introduced as a lattice compatible dynamical system involving three competing species, with the additional restriction of conserving the number of participating species.

At the mean field level a limit cycle emerges as a result of a supercritical Hopf bifurcation. When the system is realised on 2D lattice via probabilistic Kinetic Monte Carlo Simulations the system demonstrates clustering of homologous species as a result of the competing interactions. The borders between the different domains develop complex fractal shapes, characteristic of competition.

When the dynamics are integrated on a ring network, chimera states are observed for parameter values away from the Hopf bifurcation. For parameter values in the spiking regime the system presents multichimera states, while as we approach bifurcation the incoherent domains merge into a single large incoherent domain which completely covers the system size as the bifurcation parameter reaches the critical point. We also show that when we introduce hierarchical gaps in the connectivity pattern travelling chimeras are observed whose travelling speed depends on the coupling constant.

Literature:

Shabunin A, Provata A "Lattice limit cycle dynamics: Influence of long-distance reactive and diffusive mixing" EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 222 (10): 2547-2557 OCT 2013

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