Qualitative analysis in a delayed Van der Pol oscillator

Miao Peng, Zhengdi Zhang, Zifang Qu and Qinsheng Bi

Physica A: Statistical Mechanics and its Applications, 2020, vol. 544, issue C

Abstract: The main purpose of this manuscript is to introduce and compare two methods for discussing the nature of Hopf bifurcation, namely, a research method combining the normal form theory and the center manifold theorem and the other method of multiple scales. Taking a delayed Van der Pol oscillator as an example, the local stability as well as the occurrence of Hopf bifurcation are explored via choosing time delay as the bifurcation parameter. On the basis of two different methods respectively, the characters of Hopf bifurcation which includes the direction of Hopf bifurcation as well as the stability of bifurcating periodic solutions are analyzed. Finally, numerical simulations supporting the theoretical findings are given, and it is observed that the results of two methods are consistent.

Keywords: Van der Pol oscillator; Time delay; Hopf bifurcation; Normal form; Center manifold; Multiple scales (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119319442

DOI: 10.1016/j.physa.2019.123482

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