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Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop

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  • Yang, Junmin
  • Han, Maoan

Abstract

In this paper, we study the number of limit cycles of some polynomial Liénard systems with a cuspidal loop and a homoclinic loop, and obtain some new results on the lower bound of the maximal number of limit cycles for these systems.

Suggested Citation

  • Yang, Junmin & Han, Maoan, 2011. "Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 269-289.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:4:p:269-289
    DOI: 10.1016/j.chaos.2011.02.008
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    Cited by:

    1. Qin, Bo-Wei & Chung, Kwok-Wai & Algaba, Antonio & Rodríguez-Luis, Alejandro J., 2020. "Analytical approximation of cuspidal loops using a nonlinear time transformation method," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    2. Wang, Jihua, 2016. "Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 30-38.
    3. Sun, Xianbo & Su, Jing & Han, Maoan, 2013. "On the number of zeros of Abelian integral for some Liénard system of type (4,3)," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 1-12.
    4. Asheghi, R. & Bakhshalizadeh, A., 2015. "Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 120-128.
    5. Liang, Feng & Han, Maoan, 2012. "Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 454-464.

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