Stability and Hopf bifurcation in van der Pol oscillators with state-dependent delayed feedback

作者：Hou, Aiyu; Guo, Shangjiang^*

来源：Nonlinear Dynamics, 2015, 79(4): 2407-2419.

DOI：10.1007/s11071-014-1821-3

• State-dependant delay
• van der Pol
• Hopf bifurcation
• Perturbation methods
• Fredholm orthogonality condition

In this paper, we consider a classical van der Pol equation with state-dependent delayed feedback. Firstly, solutions near equilibria are constructed using perturbation methods to determine the sub/supercriticality of the bifurcation and hence their stability. Then, we choose a few examples of state-dependant delay to test our analytical results by comparing them to numerical continuation.

• 出版日期2015-3
• 单位湖南大学