A numerical procedure is presented for the automatic accurate location of certain
codimension-two homoclinic singularities along curves of codimension-one homoclinic …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x;
µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and …

Bifurcation software is an essential tool in the study of dynamical systems. From the
beginning (the first packages were written in the 1970's) it was also used in the modelling …

We study the local behavior of systems near homoclinic orbits to stationary points of saddle-
focus type. We explicitly describe how a periodic orbit approaches homoclinicity and, with …

A functional differential equation (FDE) describes the evolution of a dynamical system for
which the rate of change of the state variable depends on not only the current but also the …

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 …

This paper is devoted to the analysis of bifurcations in a three-parameter unfolding of a
linear degeneracy corresponding to a triple-zero eigenvalue. We carry out the study of …

Some theorems by LP Sil'nikov, which describe the dynamics in the neighbourhood of
homoclinic orbits, bi-asymptotic to a saddle-focus, and initially proved for real analytic vector …

Dynamical bifurcation theory is concerned with the changes that occur in the global structure
of dynamical systems as parameters are varied. This book makes recent research in …