The existence and global stability of periodic solutions to coupled oscillators

Abstract

This paper is concerned with periodic solutions of coupled oscillators. A systematic method of existence and stability of periodic solutions for coupled oscillators is provided in a combined method of graph theory, coincidence degree theory and Lyapunov method. Sufficient conditions for periodicity are obtained, which can be easily checked in the real applications. Finally, a numerical example is also provided to illustrate the correctness of theoretical results.

Keywords:

• Periodic solutions
• graph theory
• coupled oscillators
• coincidence degree theory

2010 Mathematics Subject Classifications:

• 34D20
• 34C15

Acknowledgments

The authors really appreciate the anonymous reviewers for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11601445] and the Fundamental Research Funds for the Central Universities [grant number 2682020ZT109].