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In this paper, an adaptive control scheme is developed to study the dual anti-synchronization behavior between two chaotic systems with fully uncertain parameters. This adaptive anti-synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. The adaptive dual anti-synchronization between two chaotic systems are taken to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are shown to verify the results.

The adaptive dual synchronization problem of chaotic and hyperchaotic systems with fully uncertain parameters is addressed in this paper. The sufficient conditions for achieving the dual synchronization of two chaotic and hyperchaotic systems are derived based on Lyapunov stability theory. An adaptive controller associated with the parameters update rule is developed to make the states of two chaotic and hyperchaotic systems asymptotically dual synchronized. Theoretical analysis and numerical simulations are shown to verify the results.

By using two scaling matrices, the synchronization problem of different dimensional fractional order chaotic systems in different dimensions is developed in this article. The controller is designed to assure that the synchronization of two different dimensional fractional order chaotic systems is achieved using the fractional-order Lyapunov direct method. Numerical examples and computer simulations are used to validate numerically the proposed synchronization schemes.

In this article, a novel robust nonlinear controller approach is focused to study theoretically, the reduced-order synchronization phenomena of two unrelated time-delayed chaotic systems under the determined and unknown parameters. It is assumed that the two systems are perturbed by the bounded unstructured uncertainties and unknown external disturbance. Based on the Lyapunov–Krasovskii functional theory, a robust nonlinear synchronization controller is focused and a suitable Lyapunov functional is constructed so that they establish the globally asymptotical stability of the closed-loop at the origin. Subsequently, suitable adaptive laws of unknown parameters are designed to identify the unknown parameters. Finally, the effectiveness of the proposed reduced-order synchronization approach is verified by numerical simulations. A brief comparison of the present study with prior works has been given.

The epitome of this paper centers on chaos synchronization problem of different dimensional chaotic systems in different dimensions using two scaling matrices, the Lyapunov stability theory, and the stability theory of linear system. The controller is designed to assure that the synchronization of two different dimensional chaotic systems is achieved. Numerical examples and computer simulations are used to validate, numerically, the proposed synchronization schemes.

In this paper, a nonlinear control scheme is developed to study the dual anti–synchronization behavior between a pair of hyperchaotic systems. This nonlinear control controller is designed based on Lyapunov stability theory and an analytic expression of the controller is shown. The nonlinear dual anti–synchronization between a pair of hyperchoatic systems is taken as illustrative example to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are shown to verify the results.

In this paper, we demonstrate that anti-synchronization can coexist in two different hyperchaotic systems with terms of parametric uncertainty and external disturbances using the robust active sliding mode control method. By using rigorous mathematical theory, the sufficient condition is drawn for the stability of error dynamics based on the Lyapunov stability theory, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis.

In this paper, we investigate the reduced-order anti-synchronization of uncertain chaotic systems. Based upon the parameters modulation and the adaptive control techniques, we show that dynamical evolution of third-order chaotic system can be anti-synchronized with the canonical projection of a fourth-order chaotic system even though their parameters are unknown. The techniques are successfully applied to two examples: hyperchaotic Lorenz system (fourth-order) and Lorenz system (third-order); Lu hyperchaotic system (fourth-order) and Chen system (third-order). Theoretical analysis and numerical simulations are shown to verify the results.

In this Letter, an adaptive control scheme is developed to study the anti-synchronization behavior between two identical and different chaotic systems with unknown parameters. This adaptive anti-synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. The adaptive anti-synchronization between two identical systems (Chen system) and different systems (Genesio and Lu systems) are taken as two illustrative examples to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are shown to verify the results.

Based on the nonlinear control theory, the anti-synchronization between two different hyperchaotic systems is investigated. Through rigorous mathematical theory, the sufficient condition is drawn for the stability of the error dynamics, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems. Numerical simulations are performed for the hyperchaotic Chen system and the hyperchaotic Lu system to demonstrate the effectiveness of the proposed control strategy.

An anti-synchronization scheme is proposed to achieve the anti-synchronization behavior between chaotic systems with fully unknown parameters. A sliding surface and an adaptive sliding mode controller are designed to gain the anti-synchronization. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally numerical results are presented to justify the theoretical analysis.