Efficient Synchronization Between Chaotic Lorenz Systems in Unidirectional Coupling - Laureano, M.; Mendes, D. A.; Ferreira, M. A. M. (EasyChair Preprint Nº 9872, 2025)
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.