Homoclinic saddle to saddle-focus transitions in 4D systems
Abstract
A saddle to saddle-focus homoclinic transition when the stable leading eigenspace is 3-dimensional (called the 3DL bifurcation) is analyzed. Here a pair of complex eigenvalues and a real eigenvalue exchange their position relative to the imaginary axis, giving rise to a 3-dimensional stable leading eigenspace. This transition is different from the standard Belyakov bifurcation, where a double real eigenvalue splits either into a pair of complex-conjugate eigenvalues or two distinct real eigenvalues. In the wild case, we obtain sets of codimension 1 and 2 bifurcation curves and points that asymptotically approach the 3DL bifurcation point and have a structure that differs from that the standard Belyakov case. We also give an example of this bifurcation in the wild case occuring in a perturbed Lorenz-Stenflo 4D ODE model.
Keywords
Cite
@article{arxiv.1712.03212,
title = {Homoclinic saddle to saddle-focus transitions in 4D systems},
author = {Manu Kalia and Yuri A. Kuznetsov and Hil G. E. Meijer},
journal= {arXiv preprint arXiv:1712.03212},
year = {2017}
}