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Limit Cycle Bifurcations from a Nilpotent Focus or Center of Planar Systems

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  • Maoan Han
  • Valery G. Romanovski

Abstract

We study analytic properties of the Poincaré return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this kind of systems and obtain some new results on the lower and upper bounds of the maximal number of limit cycles bifurcating from the nilpotent focus or center. The main results generalize the classical Hopf bifurcation theory and establish the new bifurcation theory for the nilpotent case.

Suggested Citation

  • Maoan Han & Valery G. Romanovski, 2012. "Limit Cycle Bifurcations from a Nilpotent Focus or Center of Planar Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-28, November.
    • Handle: RePEc:hin:jnlaaa:720830
    DOI: 10.1155/2012/720830
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    Cited by:

    1. Huzak, Renato & Vlah, Domagoj & Žubrinić, Darko & Županović, Vesna, 2023. "Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).

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