Stability analysis for coupled systems with time-varying coupling structure

• Main Authors: Jiqiang Feng, Xiaojia Luan
• Format: Article
• Language: English
• Published: SpringerOpen 2017-07-01
• Series: Advances in Difference Equations
• Subjects: time-varying coupling structure; global stability; predator-prey model; graph theory
• Online Access: http://link.springer.com/article/10.1186/s13662-017-1217-z

Abstract The stability of coupled systems with time-varying coupling structure (CSTCS) is considered in this paper. The graph-theoretic method on a digraph with constant weight has been successfully generalized into a digraph with time-varying weight. In addition, we construct a global Lyapunov function for CSTCS. By using the graph theory and the Lyapunov method, a Lyapunov-type theorem and some sufficient criteria are obtained. Furthermore, the theoretical conclusions on CSTCS can successfully be applied to the predator-prey model with time-varying dispersal. Finally, a numerical example of CSTCS is given to illustrate the effectiveness and feasibility of our results.