Abstract
In this paper, we investigate a hybrid projective combination–combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination–combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.
Highlights
Chaos is described as a nonlinear extremely complex phenomenon found in nature featuring the high sensitivity to the initial conditions
Lorenz observed that simple meteorological models depicted sensitive dependence on the initial conditions, known as butterfly effect, which established that chaos theory is widely applicable in other interdisciplinary areas
We have investigated the hybrid projective combination–combination synchronization (HPCCS) scheme among four non-identical HC systems via adaptive control method (ACM)
Summary
Chaos is described as a nonlinear extremely complex phenomenon found in nature featuring the high sensitivity to the initial conditions. Chaos synchronization among chaotic systems using adaptive control method (ACM) was introduced by Hubler [36] in 1989 for the first time. A detailed study of C–C synchronization between four non-identical chaotic systems with uncertain parameters using sliding mode control is described in Ref. C–C synchronization is generalized to n-dimensional time-delay nonlinear chaotic systems using robust adaptive sliding mode control in Ref. C–C phase synchronization between different fractional order complex nonlinear chaotic systems via active control is studied in Ref. Finite-time combination synchronization among three non-identical chaotic systems is discussed in Ref. Considering the aforementioned studies about C–C synchronization, our paper aims to investigate a hybrid projective combination–combination synchronization (HPCCS) among four non-identical HC systems via ACM. Master systems and slave systems of the C–C synchronization scheme can be identical or non-identical
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