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Nonlinear Dynamics

, Volume 75, Issue 1–2, pp 35–47 | Cite as

Stability and bifurcation analysis of delay coupled Van der Pol–Duffing oscillators

  • Hong Zang
  • Tonghua Zhang
  • Yanduo Zhang
Original Paper

Abstract

In this paper, we aim to investigate the dynamics of a system of Van der Pol–Duffing oscillators with delay coupling. First, taking the time delay as a bifurcation parameter, the stability of the equilibrium, and the existence of Hopf bifurcation are investigated. Then using the center manifold reduction technique and normal form theory, we give the direction of the Hopf bifurcation. And then by means of the symmetric bifurcation theory for delay differential equations and the representation theory of groups, we claim the bifurcation periodic solution induced by time delay is antiphase locked oscillation. Finally, at the end of the paper, numerical simulations are carried out to support our theoretical analysis.

Keywords

Coupled oscillators Phase locked oscillation Time delay 

Notes

Acknowledgements

The authors thank the referees for their valuable suggestions and comments concerning improving the work. The authors would like to acknowledge the support from National Natural Science Foundation of China (11101318 and 11001212).

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Hubei Key Lab of Intelligent RobotWuhan Institute of TechnologyWuhanChina
  2. 2.Swinburne University of TechnologyHawthornAustralia

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