Smale horseshoe

Smale Horseshoe of Cellular Neural Networks

CNN were first proposed by Chua and Yang [1988a, 1988b]. Since then much work has been done in the electricial engineering community, e.g. [Chua & Roska, 1993; Thiran et al., 1995]. The main applications of CNN are in image processing and pattern recognition, see [Chua, 1998]. A basic and important class of solutions of (1) are the stable stationary solutions of (1). It plays an important role ...

Forcing Relations for Homoclinic Orbits of the Smale Horseshoe Map

An important problem in the dynamics of surface homeomorphisms is determining the forcing relation between orbits. The forcing relation between periodic orbits can be computed using existing algorithms. Here we consider forcing relations between homoclinic orbits. We outline a general procedure for computing the forcing relation, and apply this to compute the equivalence and forcing relations f...

Research Article A 3D Smale Horseshoe in a Hyperchaotic Discrete-Time System

N ov 2 00 3 Forcing relations for homoclinic and periodic orbits of the Smale horseshoe map ∗

An important problem in the dynamics of surface homeomorphisms is determining the forcing relation between orbits. The forcing relation between periodic orbits can be computed using standard algorithms, though this does not give much information on the structure of the forcing relation. Here we consider forcing relations between homoclinic orbits, and their relationships with periodic orbits. W...

The Morse-Smale Complex

The main aim of this paper is to present the construction of the Morse– Smale complex of a compact smooth manifold M with boundary and to establish the connection to the topology of M . This approach to connecting the analysis of an appropriate function f : M → R — respectively the dynamical system associated to such a function and a Riemannian metric g — with the topology of the manifold was i...