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 and chaos has dominated research in nonlinear dynamics for over two decades,
and numerous introductory and advanced books have been published on this subject. There …

Although mathematics ranks last in the Six Arts (rites, music, archery, chariot racing,
calligraphy and mathematics), it is used in the most practical issues and affairs. Maximally, it …

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 …

The main purpose of the present survey is to contribute to the theory of dynamical systems
defined by one-dimensional piecewise monotone maps. We recall some definitions known …

This survey article is concerned with the study of bifurcations of discontinuous piecewise-
smooth maps, with a special focus on the one-dimensional case. We review the literature on …

Several types of differential equations, such as delay differential equations, age-structure
models in population dynamics, evolution equations with boundary conditions, can be …

In this paper we describe how to use the bifurcation structure of static localized solutions in
one dimension, as they exist near the robust existence of stable fronts between …

In this work, singular perturbation problems with a certain type of turning point are studied
from a geometric point of view. We first describe the delay phenomenon, initially studied by …