Razumikhin method to stability of delay coupled systems with hybrid switching diffusions

Delay coupled systems have received a great deal of attention in recent years. However, delay coupled systems with hybrid switching diffusions (DCSHSD) have rarely been discussed and are still important. Thus, this paper is devoted to studying the stability of DCSHSD based on Razumikhin method. Then...

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Bibliographic Details
Published in:Nonlinear analysis. Hybrid systems 2020-11, Vol.38, p.100934, Article 100934
Main Authors: Zhou, Hui, Song, Jin, Li, Wenxue
Format: Article
Language:English
Subjects:
Delay coupled systems
Graph theory
Hybrid switching diffusions
Razumikhin method
Stability
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Summary:Delay coupled systems have received a great deal of attention in recent years. However, delay coupled systems with hybrid switching diffusions (DCSHSD) have rarely been discussed and are still important. Thus, this paper is devoted to studying the stability of DCSHSD based on Razumikhin method. Then, combining Lyapunov method with graph theory, pth moment exponential stability of DCSHSD is studied and three kinds of stability criteria, including the Razumikhin-type theorem, the Lyapunov-type theorem and a coefficients-type theorem, are obtained. Wherein, an upper bound of Lyapunov exponent is estimated. In particular, as a practical application of our theoretical results, stability of delay coupled oscillators with hybrid switching diffusions is studied. Finally, a numerical example is provided to demonstrate the validity and feasibility of the theoretical results.
ISSN:1751-570X
DOI:10.1016/j.nahs.2020.100934