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

Volume 17, Issue 2, pp 278-287

Publication Date: 2017-06-15

http://dx.doi.org/10.22436/jmcs.017.02.09

### 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).

### Keywords

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

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