Pattern Prediction in Networks of Diffusively Coupled Nonlinear Systems

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

作者机构：Department of Mechanical Engineering Eindhoven University of Technology Netherlands Delft Center for Systems and Control Delft University of Technology Netherlands Department of Computer Science Catholic University of Leuven Belgium 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2018年第51卷第33期

页      面：62-67页

核心收录：

基　　金：This paper was elaborated in the UCoCoS project which has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 675080 

主　　题：Complex networks Hopf bifurcation Lyapunov methods Nonlinear systems Complex dynamical networks Coupled nonlinear systems Describing function methods Diffusion driven instability Harmonic Balance method In networks System of linear equations Theory 

摘      要：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. © 2018