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arXiv · 1810.02992

On the torus bifurcation in averaging theory

Murilo R. Cândido·Douglas D. Novaes
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Abstract

In this paper, we take advantage of the averaging theory to investigate a torus bifurcation in two-parameter families of 2D nonautonomous differential equations. Our strategy consists in looking for generic conditions on the averaged functions that ensure the existence of a curve in the parameter space characterized by a Neimark-Sacker bifurcation in the corresponding Poincaré map. A Neimark-Sacker bifurcation for planar maps consists in the birth of an invariant closed curve from a fixed point, as the fixed point changes stability. In addition, we apply our results to study a torus bifurcation in a family of 3D vector fields.

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Murilo R. Cândido, Douglas D. Novaes. 2019-06-02. On the torus bifurcation in averaging theory. https://doi.org/10.1016/j.jde.2019.10.031

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