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This paper proposes a modified adaptive sliding-mode control technique and investigates the reduced-order and increased-order synchronization between two different fractional-order chaotic systems using the master and slave system synchronization arrangement. The parameters of the master and slave systems are different and uncertain. These systems exhibit different chaotic behavior and topological properties. The dynamic behavior of the proposed synchronization schemes is more complex and unpredictable. These attributes of the proposed synchronization schemes enhance the security of the information signal in digital communication systems. The proposed switching law ensures the convergence of the error vectors to the switching surface and the feedback control signals guarantee the fast convergence of the error vectors to the origin. Lyapunov stability theory proves the asymptotic stability of the closed-loop. The paper also designs suitable parameters update laws the estimate the unknown parameters. Computer-based simulation results verify the theoretical findings.

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.

This paper proposes a new robust adaptive sliding mode control (RASMC) technique and investigates the control of chaos in the two-dimensional uncertain spin-orbit problem of Enceladus (SOPE) in the presence of external disturbances and model uncertainties. The external disturbances, model uncertainties, and nonlinear terms of the system are bounded and unknown. The proposed RASMC technique: 1) accomplishes oscillation free and fast convergence of the state variables to the origin; 2) suppresses chattering in the control inputs. The Lyapunov stability theory verifies the convergence behaviour and guarantees the robust asymptotic stability of the equilibrium point at the origin. In the sense of Lyapunov function, this article also provides parameters adaptation laws that confirm the convergence of uncertain parameters to some constants. The computer simulation results verify the theoretical findings and provide comparative analysis. The results of this study could be beneficial in the area of space sciences.

This paper investigates the problem of projective lag synchronization behavior in drive-response dynamical networks (DRDNs) with identical and non-identical nodes. An adaptive control method is designed to achieve projective lag synchronization with fully unknown parameters and unknown bounded disturbances. These parameters were estimated by adaptive laws obtained by Lyapunov stability theory. Furthermore, sufficient conditions for synchronization are derived analytically using the Lyapunov stability theory and adaptive control. In addition, the unknown bounded disturbances are also overcome by the proposed control. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Simulation results show the effectiveness of the proposed method.

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, the problem of inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems is introduced and investigated. Based on a new controllers and Lyapunov stability theory, a new different nonlinear control schemes are designed to study (IFSHPS) for 2D, 3D and n-D chaotic systems in discrete-time. Theoretical analysis and numerical simulations are shown to verify the results.

This paper studies the adaptive combined synchronisation (ACS) of different unknown chaotic systems. In the proposed scheme, the state vectors of a response system synchronise with the corresponding state vectors of the combined dual drive systems. The Lyapunov stability theory proves the asymptotic stability of the closed loop system at the origin. This work provides parameter update laws that estimate the actual values of unknown parameters. Important numerical simulation is included to show the effectiveness of the propose synchronisation scheme.

In this paper, we demonstrate that the adaptive hybrid synchronization behavior can coexist in two identical and different hyperchaotic systems with terms of parametric uncertainty. By using rigorous mathematical theory, the 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 hybrid synchronization between two identical systems (hyperchaotic Lu system) and different systems (hyperchaotic Lorenz and hyperchaotic Chen 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.

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, an adaptive control scheme is developed to study the hybrid synchronization behavior between two identical and different hyperchaotic systems with unknown parameters. This adaptive hybrid 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 hybrid synchronization between two identical systems (hyperchaotic Chen system) and different systems (hyperchaotic Lorenz and hyperchaotic 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.

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.

This paper brings attention to hyperchaos anti-synchronization between two identical and different hyperchaotic systems by using adaptive control. The sufficient conditions for achieving the anti-synchronization of two hyperchaotic systems are derived based on Lyapunov stability theory. An adaptive control law and a parameter update rule for unknown parameters are introduced such that the hyperchaotic Chen system is controlled to be the hyperchaotic Lu system. Theoretical analysis and numerical simulations are shown to verify the results.

Based on the nonlinear control and Lyapunov stability theory, the anti-synchronization between two identical and different chaotic systems is investigated, where the antisynchronization can be characterized by the vanishing of the sum of relevant variables in chaotic systems, such that the Lu system is controlled to be the Lorenz system. 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.

This paper brings attention to hyperchaos anti-synchronization between two identical and distinctive hyperchaotic systems using active control theory. The sufficient conditions for achieving anti-synchronization of two high dimensional hyperchaotic systems is derived based on Lyapunov stability theory, where the controllers are designed by using the sum of relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

In this study, we investigate the problem of chaos synchronization in discrete-time dynamical systems with different structures and diverse types. Based on Lyapunov stability theory, stability of lineare systems and nonlinear control methods some synchronization criterions are presented in 2D, 3D and N-dimensional discrete-time chaotic systems. Numerical examples and computer simulations are used to show the effectiveness and the feasibility of the proposed synchronization schemes.

The antisynchronization behavior of chaotic systems with parametric uncertainties and external disturbances is explored by using robust active sliding mode control method. The sufficient conditions for achieving robust antisynchronization of two identical chaotic systems with different initial conditions and two different chaotic systems with terms of uncertainties and external disturbances are derived based on the Lyapunov stability theory. Analysis and numerical simulations are shown for validation purposes.

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.

This paper centers on the chaos anti-synchronization between two identical or different chaotic systems using adaptive control. The sufficient conditions for achieving the anti-synchronization of two chaotic systems are derived based on Lyapunov stability theory. An adaptive control law and a parameter update rule for unknown parameters are introduced such that the Chen system is controlled to be the Lorenz system. Theoretical analysis and numerical simulations are shown to verify the results.