A model for the analysis of the dynamical consequences of a nontransversal intersection of the two-dimensional manifolds involved in a T-point

Abstract

The existence of a curve of homoclinic connections that bi-spirals around a T-point has been recently reported in an autonomous three-dimensional system. In this Letter we propose a model that considers a nontransversal intersection between the two-dimensional manifolds of the saddle-focus equilibria involved in such a T-point. The study of this model shows the presence of bi-spiraling curves of homoclinic connections in the parameter plane. The predictions deduced from this model strongly agree with the numerical results obtained in Rössler equations and in a modified van der Pol–Duffing electronic oscillator.