Quadratic systems with homoclinic cycles described by quintic curves.
Zheng, Yanhong, Li, Xuepeng (2001)
Applied Mathematics E-Notes [electronic only]
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Displaying similar documents to “Cubic and quartic planar differential systems with exact algebraic limit cycles.”
Quadratic systems with homoclinic cycles described by quintic curves.
An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system
Makoto Hayashi (2020)
Archivum Mathematicum
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In this paper, an improvement of the global region for the non-existence of limit cycles of the Bogdanov-Takens system, which is well-known in the Bifurcation Theory, is given by two ideas. The first is to apply the existence of the algebraic invariant curve of the system to the Bendixson-Dulac criterion, and the second is to consider a necessary condition in order that a closed orbit of the system includes two equilibrium points. In virtue of these methods, it shall be shown that our...
Five limit cycles for a simple cubic system.
Noel G. Lloyd, Jane M. Pearson (1997)
Publicacions Matemàtiques
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We resolve the centre-focus problem for a specific class of cubic systems and determine the number of limit cycles which can bifurcate from a fine focus. We also describe the methods which we have developed to investigate these questions in general. These involve extensive use of Computer Algebra; we have chosen to use REDUCE.
Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four
Eduardo Sáez, Eduardo Stange, Iván Szántó (2007)
Czechoslovak Mathematical Journal
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A class of degree four differential systems that have an invariant conic , , is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.
Uniqueness of limit cycles bounded by two invariant parabolas
Eduardo Sáez, Iván Szántó (2012)
Applications of Mathematics
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In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.
Note on curves in a jacobian
Elisabetta Colombo, Bert Van Geemen (1993)
Compositio Mathematica
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Limit cycles for a class of polynomial systems and applications.
Feng, Hanying, Xu, Rui, Liu, Qiming, Yang, Pinghua (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Uniqueness of limit cycles for a class of cubic systems with two invariant straight lines.
Xie, Xiangdong, Chen, Fengde, Zhan, Qingyi (2010)
Discrete Dynamics in Nature and Society
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