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Limit cycles in generalized Liénard systems

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  • Yu, P.
  • Han, M.

Abstract

This paper presents some new results which we obtained recently for the study of limit cycles of nonlinear dynamical systems. Particular attention is given to small limit cycles of generalized Liénard systems in the vicinity of the origin. New results for a number of cases of the Liénard systems are presented with the Hilbert number, H^(i,j)=H^(j,i), for j=4, i=10,11,12,13; j=5, i=6,7,8,9; and j=6, i=5,6. Detailed proofs for the existence of limit cycles are given in four cases.

Suggested Citation

  • Yu, P. & Han, M., 2006. "Limit cycles in generalized Liénard systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1048-1068.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:5:p:1048-1068
    DOI: 10.1016/j.chaos.2005.09.008
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    References listed on IDEAS

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    1. Yu, P. & Han, M., 2005. "Small limit cycles bifurcating from fine focus points in cubic order Z2-equivariant vector fields," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 329-348.
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    Cited by:

    1. García, Belén & Llibre, Jaume & Pérez del Río, Jesús S., 2014. "Limit cycles of generalized Liénard polynomial differential systems via averaging theory," Chaos, Solitons & Fractals, Elsevier, vol. 62, pages 1-9.
    2. Llibre, Jaume & Valls, Clàudia, 2013. "Limit cycles for a generalization of polynomial Liénard differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 65-74.

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