Cubic and quartic planar differential systems with exact algebraic limit cycles.

Bendjeddou, Ahmed; Cheurfa, Rachid

Displaying similar documents to “Cubic and quartic planar differential systems with exact algebraic limit cycles.”

Quadratic systems with homoclinic cycles described by quintic curves.

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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 $x^{2} + C y^{2} = 1$ , $C \in ℝ$ , 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.