Multi-switching Synchronization Research Articles

Exploring the Different Order of Switches During Multi-switching Synchronization

Exploring the Different Order of Switches During Multi-switching Synchronization

General multi-switching synchronization using sliding mode control

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.

The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System with Stochastic Disturbances and Unknown Parameters

This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part considers that the drive-response systems have the same or different dimensions. Firstly, a FO sliding surface is established in terms of the fractional calculus. Secondly, depending on the FO Lyapunov stability theory and the sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed. They can ensure that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed, and the upper bound values of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the scheme via MATLAB.

Analysis, circuit implementation and synchronization control of a hyperchaotic system

A four-dimensional autonomous hyperchaotic system is constructed, and the basic characteristics of the system are studied by the power spectrum, Poincaré maps, 0–1 test and Lyapunov exponents. The system has rich dynamical behaviors, such as bursting oscillations, offset boosting, transient chaos, intermittent chaos and coexistence of attractors. In addition, by studying the coexisting phenomenon and spectral entropy (SE) complexity of different initial values, an initial value that is more suitable for chaotic secure communication is selected. The circuit simulation of the system using Multisim and then the actual hardware implementation of the system by Field Programmable Gate Array (FPGA), these prove the practical existence of the system. Finally, combining the methods of backstepping control, multi-switching synchronization and synchronization of different systems, a set of controllers are proposed which can realize the backstepping multi-switching synchronization of this system with a memristive chaotic system.

General type-2 fuzzy multi-switching synchronization of fractional-order chaotic systems

In this study, the problem of multi-switching synchronization of the chaotic systems (CSs) with fractional-order dynamics is considered. Unlike to the most studies, the dynamics of slave chaotic systems are unknown and also the master systems are not fixed but are switched between several synchronization modes. A general type-2 (GT2) fuzzy neural network (FNN) is proposed to approximate the unknown nonlinearities. The stability and robustness is investigated by the Lyapunov theorem and the fractional-order adaptation laws are obtained to optimize the rules of GT2FNNs. The robustness of the proposed scheme against approximation errors and variation of synchronization modes is guaranteed by the proposed compensators. The good performance of schemed method is demonstrated by several simulations and comparison with recent presented control techniques.

New PID Controller Design for Multi-Switching Hyperchaotic Synchronization with Real-World Application

New PID Controller Design for Multi-Switching Hyperchaotic Synchronization with Real-World Application

Robust Adaptive Multi-Switching Synchronization of Multiple Different Orders Unknown Chaotic Systems

Multi-switching synchronization (MSS) of multiple different orders unknown chaotic (UC) systems confines hacking in the digital transmission process. Similarly, the suppression of undesirable chattering increases synchronization performance. This paper proposes a new robust synchronization control (RASC) technique and discusses the MSS of multiple different orders UC systems. This controller accomplishes (i) quick convergence, (ii) reduces the transient oscillations, and (iii) the rate of convergence decreases in the vicinity of the origin that causes the suppression of chattering. Analysis based on the Lyapunov direct method assures this convergence behavior with any positive values of the feedback gains. This work also provides parameters updated law that estimates the true values of unknown parameters. Numerical examples of five UC systems different orders are simulated. The computer based graphical results validate the efficiency and performance of the proposed RASC technique and the synchronization strategy when compare to peer works. In the simulation, the proposed synchronization strategy successfully recovers an encrypted received image on a communication channel. The article suggests some future research problems to extend the use of the proposed work.

A Generalized Analytical Approach for the Synchronization of Multiple Chaotic Systems in the Finite Time

This paper proposes a new finite-time controller that realizes multi-switching synchronization of chaotic systems with bounded disturbances using the drive and response system synchronization arrangement. The finite-time controller derives the synchronization error to zero within a specified time. The proposed controller consists of three basic terms; each of them accomplishes a distinct objective: (1) stability of the control loop, (2) smooth and fast convergence behavior of the synchronization error, and (3) disturbance rejection. This study also devises a methodology for designing the finite-time controller and describes a general approach that furnishes a systematic procedure for the analysis of the closed loop. The smooth behavior terminology introduced in (2) refers to the over-damped convergence of the synchronization error signals to zero and the synthesis of chattering-free control effort. The analysis, which assures the global stability of the closed loop, uses the second stability theorem of the Lyapunov, while the finite-time stability technique determines the finite-time convergence. This paper includes simulations of two numerical examples for the validation of the theoretical findings and discusses the comparative analysis. The proposed methodology is suitable to design controllers for a wide range of hyper(chaotic) systems. The contributions of the paper are: (1) describe an innovative generalize analytical methodology for the multi-switching combination synchronization of chaotic systems and (2) propose a novel controller design that insures the finite-time synchronization.

Multi-switching Synchronization of Different Orders: A Generalization of Increased/Reduced Order Synchronization

In this computational study, the author presents the multi-switching synchronization for different orders of drive and response systems using the adaptive sliding mode controllers. Furthermore, the author shows that increased/reduced order synchronization is a special case of multi-switching synchronization of different orders. For different switches, the Circular Restricted Three Body Problem and Lorenz chaotic systems are taken as a drive and response systems, respectively. Furthermore, in the computational study, the effects of both unknown model uncertainties and external disturbances are also considered.

Multi-Switching Combination Synchronization of Three Fractional-Order Delayed Systems

Multi-switching combination synchronization of three fractional-order delayed systems is investigated. This is a generalization of previous multi-switching combination synchronization of fractional-order systems by introducing time-delays. Based on the stability theory of linear fractional-order systems with multiple time-delays, we propose appropriate controllers to obtain multi-switching combination synchronization of three non-identical fractional-order delayed systems. In addition, the results of our numerical simulations show that they are in accordance with the theoretical analysis.

Dual Combination Combination Multiswitching Synchronization of Eight Fractional Order Hyperchaotic Non Linear Dynamical Systems

In this manuscript, we have proposed the scheme of dual combination combination multiswitching synchronization for fractional order hyperchaotic nonlinear dynamical systems. The proposed scheme has been applied to fractional order hyperchaotic systems. To verify the results, numerical simulations are carried out using Matlab by taking the hyperchaotic Lu system, Lorenz system, Chen system and the Rossler system as examples.

On multi switching compound synchronization of non identical chaotic systems

Multi switching compound synchronization (MSCOS) between four non identical chaotic systems is investigated. Chen system is considered as scaling drive system. Lorenz and Lü systems are taken as base drive systems. The compound of the multi drive system is then synchronized with Rössler response system using multi switching synchronization scheme. In MSCOS, the state variables of three drive systems synchronize with different state variables of response system, simultaneously. For suitable choice of scaling factors, switched modified function projective synchronization is obtained as a special case of MSCOS among chaotic systems. To achieve the desired synchronization among four non identical chaotic systems, sufficient condition is obtained using a nonlinear controller and Lyapunov stability theory, and corresponding theoretical proofs are given. The effectiveness of the proposed controllers is verified by numerical simulations using MATLAB.

Global Finite-Time Multi-Switching Synchronization of Externally Perturbed Chaotic Oscillators

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.

Multi-switching combination synchronization of different fractional-order non-linear dynamical systems

In this paper, multi-switching combination synchronization (MSCS) scheme has been investigated between a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen System are taken as drive systems. The combination of multi drive systems is then synchronized with the fractional-order Rössler chaotic system. In MSCS, the state variables of two drive systems synchronize with different state variables of response system, simultaneously. Based on the stability of fractional-order chaotic systems, the multi-switching combination synchronization of three fractional-order non-identical systems has been investigated. For the synchronization of three non-identical fractional-order chaotic systems suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.

Multi-switching Synchronization of Four Non-identical Hyperchaotic Systems

The paper addresses a combination synchronization scheme achieved for different switches of three master and one slave hyperchaotic systems. An asymptotically stable synchronized state is derived for different switches of master systems and slave system by using nonlinear control method and Lyapunov stability criteria. To elaborate the presented scheme Pang–Liu hyperchaotic system, Zheng hyperchaotic system and Chen hyperchaotic system are considered as master systems and Newton–Leipnik hyperchaotic system is considered as slave system. Theoretical and graphical results converge to the same conclusion which proves the efficiency of the applied approach.

Finite-time multi-switching synchronization behavior for multiple chaotic systems with network transmission mode

By considering network transmission mode, this paper addresses the finite-time multi-switching synchronization problem for two kinds of multiple chaotic systems. For multiple same-order chaotic systems, we construct the general switching rules and analyze the existence of switching cases. The presented schemes guarantee the states of each derive system to be finite-timely synchronized with the desired states of every respond system in the different transmission paths and switching sequences. For multiple different order chaotic systems, we analyze a special multi-switching hybrid synchronization behavior, where part of the states are completely synchronized and the others belong to combination synchronization. Moveover, the easily verifiable criterion is derived for such synchronization. Finally, numerical examples are given to show the effectiveness of the presented theoretical results.

Multiswitching compound antisynchronization of four chaotic systems

Based on three drive–one response system, in this article, the authors investigate a novel synchronization scheme for a class of chaotic systems. The new scheme, multiswitching compound antisynchronization (MSCoAS), is a notable extension of the earlier multiswitching schemes concerning only one drive–one response system model. The concept of multiswitching synchronization is extended to compound synchronization scheme such that the state variables of three drive systems antisynchronize with different state variables of the response system, simultaneously. The study involving multiswitching of three drive systems and one response system is first of its kind. Various switched modified function projective antisynchronization schemes are obtained as special cases of MSCoAS, for a suitable choice of scaling factors. Using suitable controllers and Lyapunov stability theory, sufficient condition is obtained to achieve MSCoAS between four chaotic systems and the corresponding theoretical proof is given. Numerical simulations are performed using Lorenz system in MATLAB to demonstrate the validity of the presented method.

Multi-switching compound synchronization of four different chaotic systems via active backstepping method

This manuscript presents a theoretical and numerical analysis to achieve compound synchronization of four non-identical chaotic systems for different multi-switching states. Multi-switching compound synchronization is achieved for three drive systems and one response system via active backstepping technique. By using Lyapunov stability theory, asymptotically stable synchronization states are established. To elaborate the considered scheme an example of Pehlivan system, Liu system, Qi system and Lu system is discussed. The conclusions drawn from computational and analytical approaches are in excellent agreement.

Multi-switching adaptive synchronization of two fractional-order chaotic systems with different structure and different order

In this work, we combine the active and adaptive control theories, and propose a novel synchronization scheme for a class of fractional-order chaotic systems with different structure and different order. Based on the new version of fractional-order Lyapunov stability theory, we design the adaptive controllers and updating laws of different switching. We use the fractional-order Lorenz chaotic system and the fractional-order Chen chaotic system as examples to analyze the multi-switching synchronization process for fractional-order chaotic systems with different structures and different orders. Finally, numerical simulations are also given to illustrate the effectiveness and validation of the proposed method, and the model uncertainties and external disturbances are added to the considered systems to verify the robustness of the proposed controllers.

Dual combination combination multi switching synchronization of eight chaotic systems

In this paper, a novel scheme for synchronizing four drive and four response systems is proposed by the authors. The idea of multi switching and dual combination synchronization is extended to dual combination-combination multi switching synchronization involving eight chaotic systems and is a first of its kind. Due to the multiple combination of chaotic systems and multi switching the resultant dynamic behaviour is so complex that, in communication theory, transmission and security of the resultant signal is more effective. Using Lyapunov stability theory, sufficient conditions are achieved and suitable controllers are designed to realise the desired synchronization. Corresponding theoretical analysis is presented and numerical simulations performed to demonstrate the effectiveness of the proposed scheme.