Abstract
ABSTRACTIn this article, the authors have studied combination projective synchronization using active backstepping method. The main contribution of this effort is realization of the projective synchronization between two drive systems and one response system. We relax some limitations of previous work, where only combination complete synchronization has been investigated. According to Lyapunov stability theory and active backstepping design method, the corresponding controllers are designed to observe combination projective synchronization among three different classical chaotic systems, i.e. the Lorenz system, Rössler system and Chen system. The numerical simulation examples verify the effectiveness of the theoretical analysis. Combination projective synchronization has stronger anti-attack ability and anti-translated ability than the normal projective synchronization scheme realized by one drive and one response system in secure communication.
Highlights
Chaos systems are nonlinear dynamical systems that are highly sensitive to initial conditions
Modelling the dynamics of chaotic systems is a challenging problem with important real-world application, such as weather forecast [1,2,3], road traffic [4,5], stock market returns [6], etc
As a key technique of secure communication, chaos synchronization has been extensively studied in recent decades and different notations have been proposed and studied, such as complete synchronization [7,8,9], generalized synchronization [10,11], phase synchronization [12,13], anti-phase synchronization [14,15,16] and projective synchronization [17,18,19,20]
Summary
Chaos systems are nonlinear dynamical systems that are highly sensitive to initial conditions. Chaotic systems are likely to lead completely different trajectories because of slight errors. In the late twentieth century, when the computational techniques became an important scientific tool, many scientists focused their efforts on developing deterministic methods to synchronize chaotic systems. As a key technique of secure communication, chaos synchronization has been extensively studied in recent decades and different notations have been proposed and studied, such as complete synchronization [7,8,9], generalized synchronization [10,11], phase synchronization [12,13], anti-phase synchronization [14,15,16] and projective synchronization [17,18,19,20]
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