We study a homoclinic network associated to a nonresonant hyperbolic bifocus. It is proved
that on combining rotation with a nondegeneracy condition concerning the intersection of …

There are few explicit examples in the literature of vector fields exhibiting observable chaos
that may be proved analytically. This paper reports numerical experiments performed for an …

In this paper we present a comprehensive mechanism for the emergence of strange
attractors in a two-parametric family of differential equations acting on a three-dimensional …

Modelling chaotic and intermittent behaviour, namely the excursions and reversals of the
geomagnetic field, is a big problem far from being solved. Armbruster et al.[5] considered …

There are few explicit examples in the literature of vector fields exhibiting complex dynamics
that may be proved analytically. We construct explicitly a two parameter family of vector …

What set does an experimenter see while he simulating numerically the dynamics near a
Bykov cycle? In this paper, we discuss the fate of typical trajectories near a Bykov cycle for a …

In this paper we present a mechanism for the emergence of strange attractors in a one-
parameter family of differential equations acting on a 3-dimensional sphere. When the …

We consider nonwandering dynamics near heteroclinic cycles between two hyperbolic
equilibria. The constituting heteroclinic connections are assumed to be such that one of …

This article presents a mechanism for the coexistence of hyperbolic and non-hyperbolic
dynamics arising in a neighbourhood of a Bykov cycle where trajectories turn in opposite …

We study the dynamics near heteroclinic networks for which all eigenvalues of the
linearization at the equilibria are real. A common connection and an assumption on the …