Enhancing Chaos in some New Class of Dissipative Dynamical Systems

M. A. Aziz Alaoui
Depart. of Math., L.M., Le Havre University

Preprint Le Havre Univ.


We report the finding of multispiral chaotic attractors in some new piecewise-linear system of differential equations of the type Sprott. A brief discussion about equilibrium points and their stability is given. Some of the fundamental routes to chaos and bifurcation phenomena are demonstrated with various examples.

The new notions of chaotification (also called anticontrol of chaos) has recently attracted much attention. Chaotification arises when one makes a nonchaotic dynamicl system chaotic or enhances the existing chaos of a chaotic dynamical system. In this contribution, using some piecewise linear dynamical systems such as Sprott equations, we show that modification of the piecewise-linear function enhance the existing chaos, leading to various `multispiral' strange attractors of a new type. These attractors appear as a result of the combination of several `one-spiral' attractors similar to Rossler's. This is illustrated by some numerical results describing how the dynamic changes and gives rise to `multispiral attractor' as the number of segments of the piecewise-linearity increases. Bifurcation phenomena and transition from order to `multispiral-chaos' are investigated.

The Mathematical Model :

X''' + A X'' + X' = G(X)

where G is some nonlinear function, A a parameter.

Typical multispiral strange attractors exhibited by this system are displayed below.


A 6-spiral strange attractor exhibited by this system


A 8-spiral strange attractor exhibited by this system

a 10-spiral attractor

Back to the previous page

Back to Aziz Alaoui's home page