Efficient Synchronization Between Chaotic Lorenz Systems in Unidirectional Coupling

EasyChair Preprint 9872

Abstract

In order to obtain asymptotical synchronization, we combine activepassive
decomposition for several driver signals, negative feedback control
and dislocated negative feedback control with partial replacement on the
nonlinear terms of the response system, a coupling version that was less
explored. All these unidirectional coupling schemes are established between
Lorenz systems with chaotic behavior/with control parameters that lead to
chaotic behavior.
The sufficient conditions of global stable synchronization are obtained
from a different approach of the Lyapynov direct method for the transversal
system. In one coupling we apply a result based on classification of the
symmetric matrix AT+A as negative definite, where A is the matrix characterizing
the transversal system. In other couplings the sufficient conditions
are based on derivative increase/accretion (quero dizer majoração da
derivada) of an appropriate Lyapunov function. In fact, the effectiveness
of a coupling between systems with equal dimension follows of the analysis
of the synchronization error and, if the system variables can be bounded by
positive constants, the derivative of an appropriate Lyapunov function can
be increased.(quero dizer majorada) as required by the Lyapynov direct
method.
In what follows we will always consider two chaotic dynamical systems,
since they are sufficient to study the essential in the proposed coupling
schemes. Our motivation for researching chaos synchronization methods
is to explore their practical application in various scientific areas, such as
physics, biology or economics.

Keyphrases: chaotic Lorenz systems, coupling, synchronization

@booklet{EasyChair:9872,
  author    = {Rosário Laureano and Diana A. Mendes and Manuel Alberto M. Ferreira},
  title     = {Efficient Synchronization Between Chaotic Lorenz Systems in Unidirectional Coupling},
  howpublished = {EasyChair Preprint 9872},
  year      = {EasyChair, 2023}}