Limit Cycles and Analytic Centers for a Family of 4n-1 Degree Systems with Generalized Nilpotent Singularities
Joint Authors
Xu, Changjin
Zhang, Cui
Wu, Yusen
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-04-06
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
With the aid of computer algebra system Mathematica 8.0 and by the integral factor method, for a family of generalized nilpotent systems, we first compute the first several quasi-Lyapunov constants, by vanishing them and rigorous proof, and then we get sufficient and necessary conditions under which the systems admit analytic centers at the origin.
In addition, we present that seven amplitude limit cycles can be created from the origin.
As an example, we give a concrete system with seven limit cycles via parameter perturbations to illustrate our conclusion.
An interesting phenomenon is that the exponent parameter n controls the singular point type of the studied system.
The main results generalize and improve the previously known results in Pan.
American Psychological Association (APA)
Wu, Yusen& Zhang, Cui& Xu, Changjin. 2015. Limit Cycles and Analytic Centers for a Family of 4n-1 Degree Systems with Generalized Nilpotent Singularities. Journal of Function Spaces،Vol. 2015, no. 2015, pp.1-7.
https://search.emarefa.net/detail/BIM-1068330
Modern Language Association (MLA)
Wu, Yusen…[et al.]. Limit Cycles and Analytic Centers for a Family of 4n-1 Degree Systems with Generalized Nilpotent Singularities. Journal of Function Spaces No. 2015 (2015), pp.1-7.
https://search.emarefa.net/detail/BIM-1068330
American Medical Association (AMA)
Wu, Yusen& Zhang, Cui& Xu, Changjin. Limit Cycles and Analytic Centers for a Family of 4n-1 Degree Systems with Generalized Nilpotent Singularities. Journal of Function Spaces. 2015. Vol. 2015, no. 2015, pp.1-7.
https://search.emarefa.net/detail/BIM-1068330
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1068330