Periodic solutions for neutral coupled oscillators network with feedback and time-varying delay

Abstract

This paper is considered to be about the existence of periodic solutions for neutral coupled oscillators network with feedback control and time-varying delay (NCONFT). Based on the systematic method which is firstly applied for NCONFT and consisting of coincidence degree theory, graph theory, and Lyapunov method, some sufficient criteria are obtained to verify the existence of periodic solutions for NCONFT. What’s more, how coupling topology, feedback control, and time-varying delay affect the existence of periodic solutions for NCONFT can be shown by these sufficient criteria. Finally, a numerical simulation is offered to illustrate the effectiveness of our results.

Keywords:

• Periodic solutions
• coupled oscillators network
• coincidence degree theory
• graph theory
• Lyapunov method

AMS Subject Classification:

• 93C10

Acknowledgements

The authors would like to thank the anonymous referees for the helpful comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Science Foundation of China [grant number 11271100], [grant number 11301112]; the Fundamental Research Funds for the Central Universities [grant number HIT. IBRSEM. A. 201412]; Harbin Science and Technology Innovative Talents Project of Special Fund [grant number 2013RFXYJ044].