A New Type of Combination Synchronization among Multiple Chaotic Systems

Abstract

Based on former combination synchronization studies, a new type of combination synchronization approach is developed in this research, with the consideration of parallel combination of drive systems. This new synchronization approach is referred to as combination synchronization-II. As a representative case, the combination synchronization-II between three drive systems and one response system is studied. Applying Lyapunov stability theorem and active backstepping design, sufficient conditions for the proposed combination synchronization approach are derived. Numerical simulations are performed to show the feasibility and effectiveness of the proposed approach. Based on the investigation in this research, the proposed approach provides an applicable method for designing universal combination synchronization among multiple chaotic systems.

Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

“…The synchronization problem of four systems was studied in Reference 16 by using active backstepping technique. Reference 17 developed a combination‐combination synchronization scheme for a kind of 4‐D autonomous hyperchaotic system.…”

“…However, it can be found that the scaling functions given in References 16–22 are constants or fixed functions. This means that once the synchronization scheme is given, the scaling functions are specified and can be expressed exactly.…”

“…The main contributions and innovative of this paper are as follows: Differ from the existing works, 19–24 this paper presents a new fixed time stability theorem which plays an important role on the synchronization scheme. Furthermore, the estimation of convergence time can be determined by a simple calculate formula. The scaling functions given in References 16–22 are constants or fixed functions, while the scaling functions in our combination synchronization are governed by the chaotic dynamic systems, which can improve the security of information transformation to some extent. Compare to the traditional synchronization schemes in References 5,12–22, a novel fixed time function combination synchronization scheme for the chaotic systems is developed in this work via adaptive control, and the upper bound of convergence time is fixed which is determined by the control parameters regardless of initial conditions. …”

“…The scaling functions given in References 16–22 are constants or fixed functions, while the scaling functions in our combination synchronization are governed by the chaotic dynamic systems, which can improve the security of information transformation to some extent.…”

“…Compare to the traditional synchronization schemes in References 5,12–22, a novel fixed time function combination synchronization scheme for the chaotic systems is developed in this work via adaptive control, and the upper bound of convergence time is fixed which is determined by the control parameters regardless of initial conditions.…”