Types Of Chaotic Attractors Research Articles

Fractal features of invariant sets in a three-dimensional map

A three dimensional (3D) map with spheroidal dynamics is studied. The map exhibits all known types of attracting dynamics possible in 3D state space. Furthermore, the map allows explicit manipulation of stability features. Thus, spheroidal attractors can be turned into spheroidal repellers or basin boundaries of locally similar topological properties. The link between chaotic dynamics and fractal structures is illustrated with the aid of basin boundaries corresponding to the three different types of chaotic attractors with one positive Lyapunov characteristic exponent.

Three Types of Chaotic Attractors in 3 D Maps

Abstract Coupling a one-dimensional chaotic forcing to a stable fixed point in the plane may generate different fractal attractors embedded in three dimensions. The system with real eigenvalues of the fixed point gives rise to simple chaotic attractors with three different types of fractal structures. We show that the competition of local exponents provides a generic criterion for the classification of the fractal structures in dynamical systems.