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

Maoan Han | Zendy; Valery G. Romanovski | Zendy

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

Author(s) -

Maoan Han,

Valery G. Romanovski

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/720830

Subject(s) - mathematics , nilpotent , limit cycle , limit (mathematics) , focus (optics) , bifurcation , hopf bifurcation , planar , infinite period bifurcation , center (category theory) , bifurcation theory , pure mathematics , mathematical analysis , chemistry , physics , computer graphics (images) , nonlinear system , quantum mechanics , computer science , optics , crystallography

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

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