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CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS
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作者 HuangWentao LiuYirong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第2期167-177,共11页
The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine ... The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin. 展开更多
关键词 fifth degree system focal value singular point quantity center conditions bifurcation of limit cycles.
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Uniform isochronous center of a class of higher degree polynomial differential systems
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作者 ZHOU Zheng-xin LU Fei-fei 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2024年第4期614-627,共14页
In this paper,we give the necessary and sufficient conditions for a class of higher degree polynomial systems to have a uniform isochronous center.At the same time,we prove that for this system the composition conject... In this paper,we give the necessary and sufficient conditions for a class of higher degree polynomial systems to have a uniform isochronous center.At the same time,we prove that for this system the composition conjecture is correct. 展开更多
关键词 composition conjecture center condition uniform isochronous center
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Computation of focus quantities of three-dimensional polynomial systems 被引量:1
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作者 Valery G.Romanovski Douglas S.Shafer 《上海师范大学学报(自然科学版)》 2014年第5期529-544,共16页
Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a loc... Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a local analytic first integral,which then defines a local center manifold of the system. Conditions for existence of a first integral are given by the vanishing certain polynomial or rational functions in the coefficients of the system called focus quantities. In this paper we prove that the focus quantities have a structure analogous to that in the two-dimensional case and use it to formulate an efficient algorithm for computing them. 展开更多
关键词 INTEGRABILITY center conditions focus quantities
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Solution of Center-Focus Problem for a Class of Cubic Systems
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作者 Bo SANG Chuanze NIU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第1期149-160,共12页
For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a pa... For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a particular system are considered. They show that the system has a center at the origin if and only if the first seven Liapunov constants vanish, and cannot have an isochronous center at the origin. 展开更多
关键词 center variety Isochronous center center conditions Integrating factor
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