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Singular limit cycle bifurcations to closed orbits and invariant tori

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  • Ye, Zhiyong
  • Han, Maoan

Abstract

This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed.

Suggested Citation

  • Ye, Zhiyong & Han, Maoan, 2006. "Singular limit cycle bifurcations to closed orbits and invariant tori," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 758-767.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:3:p:758-767
    DOI: 10.1016/j.chaos.2005.04.046
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    References listed on IDEAS

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    1. Chen, Xianfeng & Yu, Pei & Han, Maoan & Zhang, Weijiang, 2005. "Canard solutions of two-dimensional singularly perturbed systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 915-927.
    2. 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.
    3. Liu, Xuanliang & Han, Maoan, 2005. "Poincaré bifurcation of a three-dimensional system," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1385-1398.
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    Cited by:

    1. Singh, Vimal, 2007. "A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 813-816.
    2. Singh, Vimal, 2008. "Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 677-681.
    3. Singh, Vimal, 2008. "Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 178-183.

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