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Synchronization of chaotic systems by means of the combination of drive‐response/master–slave systems have been widely utilized. In the current study, the author introduces the concept of internal synchronization (IS) that is based on the synchronization within the system among the subsystems. Furthermore, the two types of Internal Multi‐Switching Synchronization (IMSS): the first one based on single error while the other one is based on two errors, have been discussed. In order to demonstrate, the author chooses the Lorenz Chaotic System (LCS) and Lorenz Hyper Chaotic System (LHCS) together with the adaptive sliding mode control (SMC) technique in multi‐switching manner. In addition, the efficiency of the IMSS is illustrated using Mathematica. The computational part is the witness of the achievement of stability of the IS. [ABSTRACT FROM AUTHOR]

This paper mainly deals on the issue of a chaotic synchronization of a master and slave systems. It is generally the requirement of the synchronization that someone needs at least one to one master and slave systems. In the current study, the authors introduce the concept of a synchronization in which there is no need of slave/response system externally. Furthermore, the synchronization has been demonstrated here within a system among the subsystems of different orders. In addition, adaptive control is chosen for the synchronization among various combinations in multiswitching manner. For demonstration purpose, Lorenz Six Dimensional Hyper Chaotic System (L6DHCS) is chosen. There are three different kinds of possible switches presented by the authors formed within the considered system. The numerical simulations are carried out to validate the effectiveness of the analytical technique using Mathematica. [ABSTRACT FROM AUTHOR]

Chaotic synchronization is a self-organizing phenomenon that occurs when two or more chaotic systems become synchronized. So far for multi-switching synchronization (MSS), only a homogeneous kind of switches have been discussed. This paper presents a generalized approach to MSS in which all possible heterogeneous combinations are presented. This generalization of MSS allows for greater flexibility and robustness in the MSS process. The switches are designed based on the order of the drive/response subsystems. The author also uses sliding mode control to achieve synchronization among various heterogeneous combinations during MSS. To demonstrate the effectiveness of the proposed approach, the author uses the Lorenz hyper chaotic system (LHCS) and the Chen hyper chaotic system (CHCS). The four different heterogeneous types of switches are designed and demonstrated for the chosen hyper chaotic systems. Mathematica is used for all numerical simulations. The results show that the proposed approach can achieve synchronization between two hyper chaotic systems with high accuracy. The author also shows that the proposed approach is robust to change in the parameters of the systems. This paper provides a new approach to chaotic synchronization that has potential applications in a variety of fields. The results presented in this paper are an important step towards the development of more robust and flexible synchronization schemes. [ABSTRACT FROM AUTHOR]

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]

Quick recovery of the information signals in secure communications restricts the hacking duration. The short synchronization convergence time is a crucial parameter for faster recovery. This paper develops a novel nonlinear finite-time synchronization control algorithm. This controller accomplishes the global finite-time multi-switching synchronization between two externally perturbed chaotic systems in the drive-response system synchronization scheme. The proposed controller assures the global convergence of the error dynamics in finite-time based on the Lyapunov theory. This implicitly guarantees the global stability of the closed loop. This paper considers Lp(0 < p < 1) norm inequality for the construction of the Lyapunov function. This method provides a means to determine the parameters of the proposed finite-time controller. This paper also studies the significance of structural components of the proposed controller that are responsible for the finite-time synchronization convergence. Computer simulation results of ‘two identical chaotic Lorenz systems’ and ‘chaotic Lorenz and Chen systems’ validate the theoretical findings. The paper discusses the simulation results and compares them with peer works as well. [ABSTRACT FROM AUTHOR]

Chaos synchronization is a procedure where one chaotic oscillator is forced to adjust the properties of another chaotic oscillator for all future states. This research paper studies and investigates the global chaos synchronization problem of two identical chaotic systems and two non-identical chaotic systems using the linear active control technique. Based on the Lyapunov stability theory and using the linear active control technique, the stabilizing controllers are designed for asymptotically global stability of the closed-loop system for both identical and non-identical synchronization. Numerical simulations and graphs are imparted to justify the efficiency and effectiveness of the proposed scheme. All simulations have been done by using mathematica 9. © 2014 Wiley Periodicals, Inc. Complexity 21: 379-386, 2015 [ABSTRACT FROM AUTHOR]

This paper addresses the chaos control and synchronization problems of a hyperchaotic system. It is assumed that the parameters of the hyperchaotic system are unknown and the system is perturbed by the external disturbance. Based on the Lyapunov stability theory and the adaptive control theory, suitable nonlinear controllers are designed for the asymptotic stability of the closed-loop system both for stabilization of hyperchaos at the origin and complete synchronization of two identical hyperchaotic systems. Accordingly, suitable update laws are proposed to estimate the fully uncertain parameters. All simulation results are carried out to validate the effectiveness of the theoretical findings. The effect of external disturbance is under our discussion. [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]