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Recovering Trajectories of Chaotic Piecewise Linear Dynamical Systems

M. A. Aziz Alaoui

*Depart. of Math., L.M., LeHavre University*
Fedorenko, A.

*
Institute of Math., National Academy of Sciences, kiev*

Lozi R.

*
Labo. of Math., Univrsity of Nice*

Sharkovsky, A.N.

*
Institute of Math., National Academy of Sciences, kiev*

Control of Oscillations and Chaos, Proc. IEEE, vol. **2**, 230-233,
eds. F.L. Chernousko, A.L. Fradkov, (1997)

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ABSTRACT

The purpose of this paper is to present some results on
recovering trajectories of chaotic dynamical systems
from their *epsilon*-perturbed trajectories.
Such a mathematical problem appears to be equivalent
to the extraction of an information bearing signal from an input
signal, to the reduction of a noise in an input signal, etc.

Ref: M.A. Aziz Alaoui et al ,
Control of Oscillations and Chaos, Proc. IEEE, vol. **2**, 380-383,
eds. F.L. Chernousko, A.L. Fradkov, (2000).

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Introduction

When almost each trajectory of a dynamical system is Lyapunov
stable, the problem of extraction of efficient signal from input
signal in receiving system is well known and detailed methods of
solutions are available.
For a chaotic dynamical system, where there is a sensitive
dependence on initial data and every trajectory on the strange
attractor is unstable, the situation is absolutely different.
The elaboration of methods of extraction of efficient
signal from input signal (in order to reduce the noise in an
input signal, to encode/decode electronic messages for secure
communication, etc.) for chaotic dynamical system is still
a very attractive problem.
There are different approaches to investigate such a
type of task (for instance, see
Kocarev et al., Int. J. Bifurcation and Chaos, 2(3), 1992, 709-713,
and Lozi-Aziz).
Let us point out that this problem is equivalent to the
problem of recovering a trajectory {x_i}_{i=0,n}
of the system from its *epsilon*-perturbed trajectory.
{\overline{x}}_{i=0}^n.
This is the purpose of our paper in which we present some
results on recovering the trajectories of chaotic dynamical systems
(in particular, systems given by piecewise linear maps)
from their *epsilon*-perturbed trajectories.

paper in ps format
To cite this paper :
Aziz-Alaoui M.A.,
Fedorenko A.,
Lozi R.
and
Sharkovsky A.N. .
* Control of Oscillations and Chaos,Proc. IEEE, * vol. **2**, 230-233,
eds. F.L. Chernousko, A.L. Fradkov, (1997)

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