Displaying similar documents to “Higher order branching of periodic orbits from polynomial isochrones.”

Simple examples of one-parameter planar bifurcations.

Armengol Gasull, Rafel Prohens (2000)

Extracta Mathematicae

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In this paper we give simple and low degree examples of one-parameter polynomial families of planar differential equations which present generic, codimension one, isolated, compact bifurcations. In contrast with some examples which appear in the usual text books each bifurcation occurs when the bifurcation parameter is zero. We study the total number of limit cycles that the examples present and we also make their phase portraits on the Poincaré sphere.

Transformation to Liénard form.

Albarakati, W.A., Lloyd, N.G., Pearson, J.M. (2000)

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

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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.

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.