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Poincaré Bifurcations of Two Classes of Polynomial Systems

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  • Jing Wang
  • Shuliang Shui

Abstract

Using bifurcation methods and the Abelian integral, we investigate the number of the limit cycles that bifurcate from the period annulus of the singular point when we perturb the planar ordinary differential equations of the form x.=-yC(x,y), y.=xC(x,y) with an arbitrary polynomial vector field, where C(x, y) = 1 − x3 or C(x, y) = 1 − x4.

Suggested Citation

  • Jing Wang & Shuliang Shui, 2013. "Poincaré Bifurcations of Two Classes of Polynomial Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:861329
    DOI: 10.1155/2013/861329
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    References listed on IDEAS

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    1. Buică, Adriana & Llibre, Jaume, 2007. "Limit cycles of a perturbed cubic polynomial differential center," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1059-1069.
    2. Coll, Bartomeu & Llibre, Jaume & Prohens, Rafel, 2011. "Limit cycles bifurcating from a perturbed quartic center," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 317-334.
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