Abstract
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.
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Nakao, H. Complex Ginzburg-Landau equation on networks and its non-uniform dynamics. Eur. Phys. J. Spec. Top. 223, 2411–2421 (2014). https://doi.org/10.1140/epjst/e2014-02220-1
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DOI: https://doi.org/10.1140/epjst/e2014-02220-1