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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:
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