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  • 标题:Pattern Prediction in Networks of Diffusively Coupled Nonlinear Systems ⁎
  • 本地全文:下载
  • 作者:K. Rogov ; A. Pogromsky ; E. Steur
  • 期刊名称:IFAC PapersOnLine
  • 印刷版ISSN:2405-8963
  • 出版年度:2018
  • 卷号:51
  • 期号:33
  • 页码:62-67
  • DOI:10.1016/j.ifacol.2018.12.093
  • 语种:English
  • 出版社:Elsevier
  • 摘要:AbstractIn this paper, we present a method aiming at pattern prediction in networks of diffusively coupled nonlinear systems. Interconnecting several globally asymptotical stable systems into a network via diffusion can result in diffusion-driven instability phenomena, which may lead to pattern formation in coupled systems. Some of the patterns may co-exist which implies the multi-stability of the network. Multi-stability makes the application of common analysis methods, such as the direct Lyapunov method, highly involved. We develop a numerically efficient method in order to analyze the oscillatory behavior occurring in such networks. We show that the oscillations appear via a Hopf bifurcation and therefore display sinusoidal-like behavior in the neighborhood of the bifurcation point. This allows to use the describing function method in order to replace a nonlinearity by its linear approximation and then to analyze the system of linear equations by means of the multivariable harmonic balance method. The method cannot be directly applied to a network consisting of systems of any structure and here we present the multivariable harmonic balance method for networks with a general system’s structure and dynamics.
  • 关键词:KeywordsLimit Cycles in Networks of OscillatorsBifurcations in Chaotic or Complex SystemsTheoryApplications of Complex Dynamical Networks
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