Complex Ginzburg-Landau equation on networks and its non-uniform dynamics
Graduate School of Information Science and Engineering, Tokyo Institute of Technology, O-okayama 2-12-1, Meguro, Tokyo 152-8552, Japan
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Received: 6 February 2014
Revised: 26 May 2014
Published online: 9 July 2014
Dynamics of the complex Ginzburg-Landau equation describing networks of diffusively coupled limit-cycle oscillators near the Hopf bifurcation is reviewed. It is shown that the Benjamin-Feir instability destabilizes the uniformly synchronized state and leads to non-uniform pattern dynamics on general networks. Nonlinear dynamics on several network topologies, i.e., local, nonlocal, global, and random networks, are briefly illustrated by numerical simulations.
© EDP Sciences, Springer-Verlag, 2014