Pattern prediction in networks of diffusively coupled nonlinear systems

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Samenvatting

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.

Originele taal-2Engels
Pagina's (van-tot)62-67
Aantal pagina's6
TijdschriftIFAC-PapersOnLine
Volume51
Nummer van het tijdschrift33
DOI's
StatusGepubliceerd - 2018
Evenement5th IFAC Conference on Analysis and Control of Chaotic Systems (IFAC CHAOS 2018)
- Eindhoven, Nederland
Duur: 30 okt 20181 nov 2018
https://chaos2018.dc.wtb.tue.nl/

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