Pattern prediction in networks of diffusively coupled nonlinear systems

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Abstract

In 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.

Original languageEnglish
Pages (from-to)62-67
Number of pages6
JournalIFAC-PapersOnLine
Volume51
Issue number33
DOIs
Publication statusPublished - 2018
Event5th IFAC Conference on Analysis and Control of Chaotic Systems (IFAC CHAOS 2018)
- Eindhoven, Netherlands
Duration: 30 Oct 20181 Nov 2018
https://chaos2018.dc.wtb.tue.nl/

Keywords

  • Applications of Complex Dynamical Networks
  • Bifurcations in Chaotic or Complex Systems
  • Limit Cycles in Networks of Oscillators
  • Theory
  • Theory and Applications of Complex Dynamical Networks

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