Diffusion-induced instability and chaos in random oscillator networks

Details Diffusion-induced instability and chaos in random oscillator networks Diffusion-induced instability and chaos in random oscillator networks

2009-02-21

arxiv.org/abs/0902.3742v1

Phys. Rev. E 79, 036214 (2009)

Nonlinear Sciences

Pattern Formation and Solitons

6 pages, 3 figures

Scientific paper

10.1103/PhysRevE.79.036214

We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform oscillations can be linearly unstable with respect to spontaneous phase modulations due to diffusional coupling - the effect corresponding to the Benjamin-Feir instability in continuous media. Numerical investigations under this instability in random scale-free networks reveal a wealth of complex dynamical regimes, including partial amplitude death, clustering, and chaos. A dynamic mean-field theory explaining different kinds of nonlinear dynamics is constructed.

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