Multiplicity of limit cycle attractors in coupled heteroclinic cycles

Abstract

A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle attractors in the ambient phase space (i.e. not chaotic), and there exsit many limit cycles, dividing the phase space into their basins. The patterns emerge from a local law concerning the difference between the phases of oscillators. The number of patterns grows exponentially as a function of the number of oscillators.