title: Diffusion-induced instability and chaos in random oscillator networks.
abstract: 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.
authors.affiliation: Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
authors.forename: Hiroya
authors.initials: H
authors.lastname: Nakao
authors.forename: Alexander S
authors.initials: AS
authors.lastname: Mikhailov