Pattern analysis in networks of diffusively coupled lur’e systems

Kirill Rogov (Corresponding author), A.Y. (Sasha) Pogromskiy, Erik Steur, W. Michiels, Henk Nijmeijer

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Abstract

In this paper, a method for pattern analysis in networks of diffusively coupled nonlinear systems of Lur’e form is presented. We consider a class of nonlinear systems which are globally asymptotically stable in isolation. Interconnecting such systems into a network via diffusive coupling can result in persistent oscillatory behavior, which may lead to pattern formation in the coupled systems. Some of these patterns may coexist and can even all be locally stable, i.e. the network dynamics can be multistable. Multistability 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 focus on networks of Lur’e systems in which the oscillations appear via a Hopf bifurcation with the (diffusively) coupling strength as a bifurcation parameter and therefore display sinusoidal-like behavior in the neighborhood of the bifurcation point. Using the describing function method, we replace nonlinearities with their linear approximations. Then we analyze the system of linear equations by means of the multivariable harmonic balance method. We show that the multivariable harmonic balance method is able to accurately predict patterns that appear in such a network, even if multiple patterns coexist.
Original languageEnglish
Article number1950200
Number of pages17
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume29
Issue number14
DOIs
Publication statusPublished - 30 Dec 2019

Keywords

  • Periodic solutions
  • Bifurcation
  • harmonic balance
  • Nonlinear systems

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