Exponential synchronization of stochastic coupled oscillators networks with delays

Abstract

This paper investigates the exponential synchronization problem of coupled oscillators networks with disturbances and time-varying delays. On basis of graph theory and stochastic analysis theory, a feedback control law is designed to achieve exponential synchronization. By constructing a global Lyapunov function for error network, both pth moment exponential synchronization and almost sure exponential synchronization of drive-response networks are obtained. Finally, a numerical example is given to show the effectiveness of the proposed criteria.

Keywords:

• Exponential synchronization
• stochastic coupled oscillators network
• time-varying delay
• graph theory

AMS Subject Classifications:

• 60H10
• 34D06
• 34C15

Acknowledgements

The authors really appreciate the reviewers’ valuable comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the NNSF of China [grant number 11301112], [grant number 11301115], [grant number 11501148], [grant number 11171081], [grant number 11171056], China Postdoctoral Science Foundation funded project [No. 2013M541352] and the NNSF of Shandong Province [No. ZR2013AQ003 and ZR2015AQ002].