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Limit cycles in a switching Liénard system

  • * Corresponding author: Laigang Guo

    * Corresponding author: Laigang Guo

The second author is supported by the Fundamental Research Funds for the Central Universities 2021NTST32

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  • In this paper, we consider a class of quadratic switching Liénard systems with three switching lines. We give an algorithm for computing the Lyapunov constants of this system. Based on this method, we obtain a center condition and three limit cycles bifurcating from the focus $ (0,0) $. Further, an example of quadratic switching systems is constructed to show the existence of six limit cycles bifurcating from the center. This is a new low bound on the maximal number of small-amplitude limit cycles obtained in such quadratic switching systems.

    Mathematics Subject Classification: Primary: 34C05, 34C07.


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  • Figure 1.  Diagram

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