Multiplicity of Limit Cycle Attractors in Coupled Heteroclinic Cycles

Details Multiplicity of Limit Cycle Attractors in Coupled Heteroclinic Cycles Multiplicity of Limit Cycle Attractors in Coupled Heteroclinic Cycles

2002-12-09

arxiv.org/abs/nlin/0212020v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 6 figures

Scientific paper

10.1143/PTP.109.133

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 many limit cycles exist dividing the phase space as their basins. The patterns are constructed with a local law of difference of phases between the oscillators. The number of patterns grows exponentially with increasing of the number of oscillators.

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