Data, models and transitions in computational neuroscience : bottom-up and top-down approaches
Manu Kalia · 2022
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 at the critical parameter values.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 of the standard Belyakov case.We give an example of this bifurcation in a perturbed Lorenz-Stenflo 4D ODE model.