This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

We prove that the Lorenz system with appropriate choice of parameter values has a specific
type of heteroclinic cycle, called a singularly degenerate heteroclinic cycle, that consists of a …

This paper studies three-parameter unfoldings of resonant orbit flip and inclination flip
homoclinic orbits. First, all known results on codimension-two unfoldings of homoclinic flip …

Resonant homoclinic flip bifurcations are codimension-three phenomena that act as
organizing centres for codimension-two inclination flip, orbit flip and eigenvalue-resonance …

Singular Hopf bifurcation occurs in generic families of vector fields with two slow variables
and one fast variable. Prototypes for this bifurcation depend upon several parameters, and …

Homoclinic bifurcations are important phenomena that cause global rearrangements of the
dynamics in phase space, including changes to basins of attractions and the generation of …

We present a numerical method for branch switching between homoclinic orbits to equilibria
of ODEs computed via numerical continuation. Starting from a 1-homoclinic orbit our method …

When a real saddle equilibrium in a three-dimensional vector field undergoes a homoclinic
bifurcation, the associated two-dimensional invariant manifold of the equilibrium closes on …

Bursting phenomena are found in a wide variety of fast–slow systems. In this article, we
consider the Hindmarsh–Rose neuron model, where, as it is known in the literature, there …