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- Title
Stability and bifurcation analysis of delay coupled Van der Pol-Duffing oscillators.
- Authors
Zang, Hong; Zhang, Tonghua; Zhang, Yanduo
- 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.
- Subjects
VAN der Pol oscillators (Physics); HOPF bifurcations; DIFFERENTIAL equations; COMPUTER simulation; TIME delay systems; PARAMETRONS
- Publication
Nonlinear Dynamics, 2014, Vol 75, Issue 1/2, p35
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-013-1047-9