Pattern prediction in networks of diffusively coupled nonlinear systems

K. Rogov, A. Pogromsky, E. Steur, W. Michiels, H. Nijmeijer

Research output: Contribution to journalConference articleScientificpeer-review

4 Citations (Scopus)


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
Issue number33
Publication statusPublished - 2018


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


Dive into the research topics of 'Pattern prediction in networks of diffusively coupled nonlinear systems'. Together they form a unique fingerprint.

Cite this