Limit cycle bifurcations and analytic center conditions for a class of generalized nilpotent systems

Volume 17, Issue 2, pp 278-287 http://dx.doi.org/10.22436/jmcs.017.02.09

Publication Date: June 15, 2017 Submission Date: December 22, 2016

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Authors

Yusen Wu - School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023 Henan, P. R. China. Cui Zhang - School of Mathematical Science, Luoyang Normal University, Luoyang, 410022 Henan, P. R. China. Sumin Yang - School of Humanities and Science, Guangxi Technological College of Machinery and Electricity, Nanning, 530007 Guangxi, P. R. China.

Abstract

Bifurcation of limit cycles and analytic center conditions for a class of systems in which the origin is a generalized nilpotent singular point are discussed. An interesting phenomenon is that the exponent parameter \(n\) controls the singular point type of the studied system (1.1).

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Keywords

• Limit cycle bifurcation
• analytic center conditions
• generalized nilpotent systems.

MSC

•  34C05
•  37G15

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