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

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Abstract

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.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Aiyu Hou & Shangjiang Guo

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  1. Aiyu Hou
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  2. Shangjiang Guo
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Correspondence to Shangjiang Guo.

Additional information

This work supported in part by the NSFC (Grant No. 11271115), by the Doctoral Fund of Ministry of Education of China (Grant No. 20120161110018), and by the Hunan Provincial Natural Science Foundation (Grant No. 14JJ1025).

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Hou, A., Guo, S. Stability and Hopf bifurcation in van der Pol oscillators with state-dependent delayed feedback. Nonlinear Dyn 79, 2407–2419 (2015). https://doi.org/10.1007/s11071-014-1821-3

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  • DOI: https://doi.org/10.1007/s11071-014-1821-3

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