Displaying similar documents to “Branching of periodic orbits from Kukles 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.

Hoptf bifurcation from infinity for planar control systems.

Jaume Llibre, Enrique Ponce (1997)

Publicacions Matemàtiques

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Symmetric piecewise linear bi-dimensional systems are very common in control engineering. They constitute a class of non-differentiable vector fields for which classical Hopf bifurcation theorems are not applicable. For such systems, sufficient and necessary conditions for bifurcation of a limit cycle from the periodic orbit at infinity are given.