TY - JOUR
T1 - Pattern prediction in networks of diffusively coupled nonlinear systems
AU - Rogov, K.
AU - Pogromsky, A.
AU - Steur, E.
AU - Michiels, W.
AU - Nijmeijer, H.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Applications of Complex Dynamical Networks
KW - Bifurcations in Chaotic or Complex Systems
KW - Limit Cycles in Networks of Oscillators
KW - Theory
UR - http://www.scopus.com/inward/record.url?scp=85059168183&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2018.12.093
DO - 10.1016/j.ifacol.2018.12.093
M3 - Conference article
AN - SCOPUS:85059168183
SN - 2405-8963
VL - 51
SP - 62
EP - 67
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
IS - 33
ER -