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 …

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 paper is devoted to topical issues of modern mathematical theory of dynamical chaos
and its applications. At present, it is customary to assume that dynamical chaos in finite …

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 …

We provide conditions to guarantee the occurrence of Shilnikov bifurcations in analytic
unfoldings of some Hopf-Zero singularities through a beyond all order phenomenon: the …

В работе рассматриваются актуальные вопросы современной математической теории
динамического хаоса и ее приложений. В настоящее время принято считать, что в …

We introduce a one-parameter family of polymatrix replicators defined in a three-
dimensional cube and study its bifurcations. For a given interval of parameters, each …

About the unfolding of a Hopf-zero singularity Page 1 About the unfolding of a Hopf-zero
singularity Freddy Dumortier Universiteit Hasselt Campus Diepenbeek Agoralaan-Gebouw D …

Dynamical phenomena are studied near a Hopf-saddle-node bifurcation of fixed points of
3D-diffeomorphisms. The interest lies in the neighbourhood of weak resonances of the …

The main goal of this paper is to prove analytically the existence of strange attractors in a
family of vector fields consisting of two Brusselators linearly coupled by diffusion. We will …