Joint work with Prof. Alan Champneys and Dr. Bernd Krauskopf.

We present a new numerical method for homoclinic branch switching in AUTO/HomCont. This method transfers a $1$-homoclinic orbit to an $n$-homoclinic orbit, where $n>1$. Applications include studying inclination and orbit flip bifurcations, homoclinic-doubling cascades and Shil'nikov bifurcations.

This allows us to explore routes to chaos in applicable models. It also gives the possibility to reliably find multi-hump travelling waves in applications such as the FitzHugh-Nagumo nerve-axon equations and a 5th order Hamiltonian KdV model for water waves. We used Sandstede's model, a theoretical normal form like system of ordinary differential equations, as a testbed for the algorithm and later successfully applied it to the applications mentioned above. Even though this scheme is based on Lin's method, a theoretical approach, it is very robust and more reliable than traditional shooting methods, especially if the unstable manifold has a dimension higher than one. We give a demonstration of the implementation in AUTO2000.