Abstract and Applied Analysis

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

Maoan Han and Valery G. Romanovski

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 720830, 28 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475957

Digital Object Identifier
doi:10.1155/2012/720830

Mathematical Reviews number (MathSciNet)
MR2999906

Zentralblatt MATH identifier
1261.34032

Citation

Han, Maoan; Romanovski, Valery G. Limit Cycle Bifurcations from a Nilpotent Focus or Center of Planar Systems. Abstr. Appl. Anal. 2012 (2012), Article ID 720830, 28 pages. doi:10.1155/2012/720830. https://projecteuclid.org/euclid.aaa/1364475957


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