# 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.

###
Abstract

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.

**
Introduction
**
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

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