Five limit cycles for a simple cubic system.

Noel G. Lloyd; Jane M. Pearson

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Displaying similar documents to “Five limit cycles for a simple cubic system.”

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.

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.

On lopsided systems.

Javier Chavarriga, Nazim Salih (2002)

Extracta Mathematicae

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The null divergence factor.

Javier Chavarriga, Héctor Giacomini, Jaume Giné (1997)

Publicacions Matemàtiques

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Let (P,Q) be a C vector field defined in a open subset U ⊂ R. We call a null divergence factor a C solution V (x, y) of the equation P ∂V/∂x + Q ∂V/ ∂y = ( ∂P/∂x + ∂Q/∂y ) V. In previous works it has been shown that this function plays a fundamental role in the problem of the center and in the determination of the limit cycles. In this paper we show how to construct systems with a given null divergence factor. The method presented in this paper is a generalization of the classical Darboux...

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

Bendjeddou, Ahmed, Cheurfa, Rachid (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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New sufficient conditions for a center and global phase portraits for polynomial systems.

Hector Giacomini, Malick Ndiaye (1996)

Publicacions Matemàtiques

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In this paper we consider cubic polynomial systems of the form: x' = y + P(x, y), y' = −x + Q(x, y), where P and Q are polynomials of degree 3 without linear part. If M(x, y) is an integrating factor of the system, we propose its reciprocal V (x, y) = 1 / M(x,y) as a linear function of certain coefficients of the system. We find in this way several new sets of sufficient conditions for a center. The resulting integrating factors are of Darboux type and the first integrals are in the...