Globally Stable Synchronization Conditions in Total Diffusive Linear Bidirectional Coupling Between Continuous Dynamical Systems and Partial Replacement (Rössler and Lorenz)

EasyChair Preprint 9873

Abstract

In order to obtain asymptotical synchronization, we combine diffusive
linear bidirectional coupling with partial replacement on the nonlinear terms
of the second system, a coupling version that was less explored. All these
bidirectional coupling schemes are established between Lorenz systems or
Rössler 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 the remaining couplings the sufficient
conditions are based on (the) increase/accretion of derivative (quero dizer
majoração da derivada) of an appropriate Lyapunov function assuming
yet the limitation of certain variables. In fact, the effectiveness of a coupling
between systems with equal dimension follows of the analysis of the
synchronization error e(t) 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: bidirectional coupling, dynamical systems, synchronization

@booklet{EasyChair:9873,
  author    = {Rosário Laureano and Diana A. Mendes and Manuel Alberto M. Ferreira},
  title     = {Globally Stable Synchronization Conditions in Total Diffusive Linear Bidirectional Coupling Between Continuous Dynamical Systems and Partial Replacement (Rössler and Lorenz)},
  howpublished = {EasyChair Preprint 9873},
  year      = {EasyChair, 2023}}