Synchronized, Chimera and Multichimera States in Simple Cellular Automata Model of Coupled Oscillators
Amitava Banerjee, Muktish Acharyya · arXiv (Cornell University) · 2016
We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit all important collective dynamical states found in other synchronizing systems. Depending on the values of coupling strength and radius of coupling, we observed four phases namely: asynchronous, where all the oscillators oscillate incoherently, chimera, where a single group of connecting oscillators oscillates coherently and rest oscillate incoherently, the multichimera and synchronized, where all oscillators oscillate coherently. We have plotted the phase diagram in the plane described by strength of coupling and the radius of coupling using the strength of incoherence. Furthermore, the chimera and multichimera were distinguished by discontinuity measure. The phase diagrams reveal interesting properties about the nature of the synchronizing transition. The multichimera state is shown to have a power law distribution of synchronized cluster sizes, whose exponent is found to be independent of the system parameters. A criterion of persistence of chimera was developed analytically and compared with numerical simulation.