Razumikhin method to stability of delay coupled systems with hybrid switching diffusions. (November 2020)

• Record Type: Journal Article
• Authors: Zhou, Hui; Song, Jin; Li, Wenxue
• Is Part Of: Nonlinear analysis. Volume 38(2020)
• Publication Date: 2020-11
• Subjects: Hybrid switching diffusions -- Razumikhin method -- Delay coupled systems -- Stability -- Graph theory; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100934
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: 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, p th 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.