Application of Kronecker products to the analysis of systems with uniform linear coupling

Author

Wu, Chai Wah ; Chua, Leon O.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA

Volume

42

Issue

10

fYear

1995

fDate

10/1/1995 12:00:00 AM

Firstpage

775

Lastpage

778

Abstract

In this paper, we show how the Kronecker product can be useful in simplifying the notation encountered in the analysis of linearly coupled systems where the cells are identical and the coupling is uniform. We give two applications where this is useful. First we use it in the analysis of Turing patterns in reaction-diffusion systems to obtain conditions for the coupling to destabilize the uniform equilibrium point. In the second application we use the Kronecker product to obtain simple sufficient conditions for an array of linearly coupled dynamical systems to synchronize. We discuss briefly extensions to additive nonlinear coupling

Keywords

diffusion; linear systems; matrix multiplication; stability; synchronisation; Kronecker products; Turing patterns; additive nonlinear coupling; cell array; dynamical systems; equilibrium point; instability; reaction-diffusion systems; synchronization; uniform linear coupling; Circuit topology; Coupling circuits; Differential equations; Oscillators; Pattern analysis; Resistors; Sufficient conditions; Vectors;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.473586

Filename

473586