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


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.


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).