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The present study is based on the anti-synchronization of chaotic systems of different orders. The author studied the reduced-order anti-synchronization (ROAS) in order to observe the variations between the computational studies on Mathematica and Matlab. For demo purpose, circular restricted three body problem (CRTBP) and Lorenz chaotic systems of different orders are chosen. The study of ROAS has been carried out via a robust generalized active control technique under the effect of both unknown model uncertainties and external disturbances. In order to see the variations between the computational studies, a parallel simulation is carried out on Mathematica and Matlab at the same values of the parameters and initial conditions. [ABSTRACT FROM AUTHOR]

The present study deals with the synchronization of chaotic systems of different orders. The author investigates the reduced-order synchronization (ROS) problem for a circular restricted three body problem (CRTBP)-Lorenz chaotic systems that are of different orders. The study of ROS has been carried out via a robust generalized active control technique together with the effect of both unknown model uncertainties and external disturbances. Also for the chosen master-slave combination, a comparison of computational study between Mathematica and Matlab has been presented in order to observe the variations. Furthermore, it is discussed that ROS is a special case for multi-switching synchronization of different orders of chaotic systems. [ABSTRACT FROM AUTHOR]

The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/drive-response systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Nonlinear Control Techniques, based on Lyapunov stability theory. It has been shown that the proposed schemes have outstanding transient performances and that analytically as well as graphically, synchronization is asymptotically globally stable. Suitable feedback controllers are designed to stabilize the closed-loop system at the origin. All simulation results are carried out to corroborate the effectiveness of the proposed methodologies by using Mathematica 9. [ABSTRACT FROM AUTHOR]

In this computational study, we synchronize the Circular Restricted Three Body Problem (CRTBP) with Lorenz Hyper Chaotic System (LHCS) using a Robust Adaptive Sliding Mode Controller (RASMC) together with uncertainties, external disturbances and fully unknown parameters. A simple suitable sliding surface, which includes synchronization errors, is constructed and appropriate update laws are used to tackle the uncertainties, external disturbances and unknown parameters. All simulations to achieve the synchronization for the implemented technique for the two non-identical systems under consideration are being done using Mathematica. © 2013 Wiley Periodicals, Inc. Complexity 18: 58-64, 2013 [ABSTRACT FROM AUTHOR]

This article proves that the robust finite-time synchronization behavior can be achieved for the chaotic systems with different orders. Based on the Lyapunov stability theory and using the nonlinear feedback control, sufficient algebraic conditions are derived to compute the linear controller gains. These gains are then used to achieve the robust finite time increasing order and reduced order synchronization of the chaotic systems. This study also discusses the design of a controller that accomplishes the finite time synchronization of two chaotic systems of different dimensions under the effect of both unknown model uncertainties and external disturbances. Numerical simulation results are furnished to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]