Can I read Homoclinic saddle to saddle-focus transitions in 4D systems on EtoBox?

Homoclinic saddle to saddle-focus transitions in 4D systems by Kalia, Manu; Kuznetsov, Yuri A.; Meijer, Hil G. E. is a scholarly article available to read on EtoBox.

What is Homoclinic saddle to saddle-focus transitions in 4D systems about?

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.

Author

Kalia, Manu; Kuznetsov, Yuri A.; Meijer, Hil G. E.

Published

2017

Language

EN