Linearizability and critical period bifurcations of a generalized Riccati system |
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| Authors: | Valery G. Romanovski Yilei Tang Yun Tian |
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| Affiliation: | 1.Department of Mathematics,Shanghai Normal University,Shanghai,People’s Republic of China;2.Faculty of Electrical Engineering and Computer Science,University of Maribor,Maribor,Slovenia;3.Faculty of Natural Science and Mathematics,University of Maribor,Maribor,Slovenia;4.Center for Applied Mathematics and Theoretical Physics,University of Maribor,Maribor,Slovenia;5.Instituto de Ciências Matemáticas e de Computa??o - USP,S?o Carlos,Brazil;6.School of Mathematical Science,Shanghai Jiao Tong University,Shanghai,People’s Republic of China |
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| Abstract: | In this paper, we investigate the isochronicity and linearizability problem for a cubic polynomial differential system which can be considered as a generalization of the Riccati system. Conditions for isochronicity and linearizability are found. The global structure of systems of the family with an isochronous center is determined. Furthermore, we find the order of weak center and study the problem of local bifurcation of critical periods in a neighborhood of the center. |
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