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The European Physical Journal Special Topics

, Volume 223, Issue 12, pp 2411–2421 | Cite as

Complex Ginzburg-Landau equation on networks and its non-uniform dynamics

  • Hiroya Nakao
Review
Part of the following topical collections:
  1. Resilient Power Grids and Extreme Events

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.

Keywords

Hopf Bifurcation Direct Numerical Simulation European Physical Journal Special Topic Linear Growth Rate Hopf Bifurcation Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Graduate School of Information Science and Engineering, Tokyo Institute of TechnologyTokyoJapan

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