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This study introduces a brand-new, four-dimensional hyperchaotic system and provides a full analysis of its dynamical characteristics. Time series, phase portraits, Poincaré maps, bifurcation diagrams, estimating the Lyapunov exponents, and determining the Kaplan–Yorke dimension are all used to examine the system. Additionally, the system's equilibrium points are located and their stability is explored. Through the use of active, adaptive, and sliding-mode control approaches, we have also synchronized the newly introduced system. The Lyapunov stability theory and Vaidyanathan's theorem are the foundations upon which the controllers are built to guarantee synchronization between the systems. Finally, MATLAB-based numerical simulations are used to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

This study explores the challenge of achieving a fast finite-time projective synchronization (FFTPS) in chaotic systems characterized by incommensurate fractional orders, unknown master-slave models, and uncertain external disturbances. Utilizing the principles of Lyapunov stability theory, two fuzzy sliding mode control (FSMC) schemes are proposed. Accordingly, two novel non-singular finite-time sliding surfaces are constructed. Fuzzy logic systems are utilized to provide an approximation of the continuous uncertain dynamics within the master-slave system. The sufficient conditions for both controllers are derived to ensure this robust FFTPS. Finally, the proposed controllers are validated through numerical simulations on two projective synchronization examples of fractional-order chaotic systems, demonstrating their feasibility. [ABSTRACT FROM AUTHOR]

In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system's attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation. [ABSTRACT FROM AUTHOR]

A new scheme is proposed for the synchronization transmission of the chaotic signals within a quantum network composed of the Dicke models with uncertain parameters. Considering that the chattering occurrence in the existing sliding mode control technique due to the general sliding mode surface is only dependent on the error variables, we put forward the novel design strategy of the sliding mode surface which is not only related to the error variables, but also the element of differential–integral is added into the sliding mode surface, which enables the synchronization transmission technique can flexibly adjust the speed of synchronous transmission and eliminate the chattering phenomenon during the synchronous transmission of quantum chaotic signal. The simulation results illustrate that the quantum signal from a single Dicke chaotic system can be transmitted synchronously among all nodes within the designed network with arbitrary topology and node number, and simultaneously the uncertain parameters belonging to the Dicke chaotic systems are also accurately identified, indicating that the design of the signal synchronization transmission controller and the identification law of the uncertain parameters based on the modified sliding mode technique proposed in this work are reasonable and feasible. [ABSTRACT FROM AUTHOR]

Based on the fractional calculus and sliding mode control (SMC) techniques, this paper presents a predefined-time synchronization scheme for fractionalorder chaotic systems (FOCSs). Firstly, a predefined-time control method is proposed for fractional-order systems. Subsequently, a novel sliding surface is presented to ensure predefined-time convergence of the synchronization error. Then, a controller is designed by combining the predefined-time stability and the SMC method to ensure that the synchronization error converges to zero within the predefined time. Finally, the feasibility and robustness of the scheme are illustrated with two numerical simulation examples. [ABSTRACT FROM AUTHOR]

The purpose of this research is to investigate the synchronization and control for uncertain memristor-based cellular neural network and its application in secure communication. To address the issue, a novel sliding mode function is designed, on which the system states can effectively converge to the equilibrium point after reaching the sliding mode surface. Moreover, the corresponding controller is constructed by employing the proposed sliding mode function. The proposed control strategy achieves the synchronization of the uncertain memristor-based cellular neural network, and effectively addresses the integral saturation existing in traditional one. In addition, the control performance, including convergence speed, control accuracy, robustness and security, are significantly enhanced. Furthermore, the stability of the system is discussed based on Lyapunov theory. Finally, comparative tests and application examples are presented to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A robust global fuzzy sliding mode controller is designed in this paper for the synchronization of non-linear systems with control input non-linearities (CIN) and uncertainties. A consistent global fuzzy sliding mode control (GFSMC) law is developed, which guarantees the suppression of the reaching phase and the presence of the sliding phase from the initial time. Chattering phenomenon, which is characteristic of customary sliding mode control (SMC), avoided by the on-line fuzzy regulation of the sliding surface in the controller, when the system is subject to disturbances and CIN. Finite-time boundedness (FTB) properties are designed with adequate conditions, which are entrenched in terms of linear matrix inequalities (LMIs) with the help of cost and Lyapunov functions. Numerical simulations for the synchronization problem of the chaotic modified Colpitt's system and Duffing system clearly show the good performance of the proposed control scheme. The present work provides a regular procedure to design GFSMC for a class of non-linear systems with CIN. [ABSTRACT FROM AUTHOR]

This article investigates the finite/fixed‐time synchronization problem of Markovian jumping delayed chaotic recurrent neural networks with uncertainties by employing sliding mode control method. In order to cope with Markovian jump and parameter uncertainties, sliding model control is used for its strong robustness and insensitivity character to external disturbances and parameter variations. Above all, two simplified sliding mode surfaces are constructed. Following that, matching controllers are constructed to guarantee the finite/fixed‐time reachability of sliding mode surfaces. Additionally, the dynamics of the sliding mode surfaces can be achieved in a finite/fixed‐time. Based on the Lyapunov stability theory, some sufficient conditions are proposed to guarantee the finite/fixed‐time synchronization. Compared with the conclusions of the existing literature, this article generalizes the corresponding results to Markovian jump, parameter uncertainties, and nonidentical systems. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper introduces a novel adaptive nonsingular fast terminal sliding mode approach that benefits from an interval type-2 fuzzy logic estimator and a gain for control and synchronization of chaotic systems in the presence of uncertainty. The nonsingular fast terminal sliding mode controller is developed to increase the convergence rate and remove the singularity problem of the system. Using the proposed method, the finite-time convergence has been ensured. To eliminate the chattering phenomenon in the conventional sliding mode controller, the discontinuous sign function is estimated using an interval type-2 fuzzy inference system (FIS) based on the center of sets type reduction followed by defuzzification. By adding the proportionate gain to the interval type-2 FIS, the robustness and speed of the controller system is enhanced. An appropriate Lyapunov function is utilized to ensure the closed-loop stability of the control system. The performance of the controller is evaluated for a nonlinear time-varying second-order magnetic space-craft chaotic system with different initial conditions in the presence of uncertainty. The simulation results show the efficacy of the proposed approach for the tracking control problems. The time and frequency domain analysis of the control signal demonstrates that the chattering phenomenon is successfully diminished. [ABSTRACT FROM AUTHOR]

This paper presents the control design framework for the hybrid synchronization (HS) and parameter identification of the 3-cell cellular neural network. The cellular neural network (CNN) of this kind has increasing practical importance but due to its strong chaotic behavior and the presence of uncertain parameters make it difficult to design a smooth control framework. Sliding mode control (SMC) is very helpful for this kind of environment where the systems are nonlinear and have uncertain parameters and bounded disturbances. However, conventional SMC offers a dangerous chattering phenomenon, which is not acceptable in this scenario. To get chattering-free control, smooth higher-order SMC formulated on the smooth super twisting algorithm (SSTA) is proposed in this article. The stability of the sliding surface is ensured by the Lyapunov stability theory. The convergence of the error system to zero yields hybrid synchronization and the unknown parameters are computed adaptively. Finally, the results of the proposed control technique are compared with the adaptive integral sliding mode control (AISMC). Numerical simulation results validate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The synchronization control problem of a class of chaotic systems with unknown uncertainties and outside perturbation is addressed in this article by employing an innovative adaptive sliding mode controller (SM, SMC) constructed using a disturbance observer (DO). For the synchronous error system, the external disturbances estimated by the disturbance observer cannot be measured directly. If the appropriate gain matrix is chosen, the DO can approximate the unknown external disturbances well. Then a continuous adaptive SM controller based on the DO's output is designed by using adaptive techniques and the system dimensional expansion method. The Duffing-Holmes chaotic system is finally selected to numerically test the efficiency of the suggested strategy. [ABSTRACT FROM AUTHOR]

In this work, a dynamic-free adaptive sliding mode control (adaptive-SMC) methodology for the synchronization of a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation is proposed. By incorporating the frequency distributed model (FDM) and the fractional version of the Lyapunov stability theory, a dynamic-free adaptive SMC methodology is designed to effectively overcome the inherent chaotic behavior exhibited by the delayed FONNSs to achieve synchronization. Notably, the decoupling of the control laws from the nonlinear/linear dynamical components of the system is ensured, taking advantage of the norm-boundedness property of the states in chaotic systems. The effectiveness of the suggested adaptive-SMC method for chaos synchronization in delayed fractional-order Hopfield neural network systems is validated through numerical simulations, demonstrating its robustness and efficiency. The proposed dynamic-free adaptive-SMC approach, incorporating the FDM and fractional Lyapunov stability theorem, offers a promising solution for synchronizing chaotic delayed FONNSs with input saturation, with potential applications in various domains requiring synchronization of such systems. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Zhejiang University (Science Edition) is the property of Journal of Zhejiang University (Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, based on integer-order Hindmarsh–Rose (HR) neurons under an electric field, the fractional-order model is constructed, and the nonlinear term is decomposed by the Adomian decomposition method, and the numerical solution of the system is obtained. The firing behavior of the neuron model is analyzed by using a phase diagram, interspike interval (ISI) bifurcation diagram, sample entropy (SE) complexity, and largest Lyapunov exponent (LLE). Based on the sliding mode control theory, a chaos synchronization controller of the system is designed. Matlab simulation results show that the controller is realizable and effective, and also has the characteristic of fast response, which provides a reference for the control and application of a memristor neural network system. [ABSTRACT FROM AUTHOR]

Despite that the synchronization of chaotic systems has been extensively investigated and demonstrated to contribute to physical, chemical, financial, and biological applications, the synchronization of different perturbed bistable systems appears to be an open issue. This is significant with the fact that the bistability widely exists from the visual perception to the electrical and mechanical systems. Therefore, this paper proposes a continuous finite-time terminal sliding mode control method to synchronize two bistable electromechanical transducers, with the electrostatic one acting as the master system and the piezoelectric one acting as the slave system. The model of two systems as well as the control method considering external disturbances and unmodeled dynamics are presented. Numerical simulation results show that two bistable systems can be synchronized with our proposed control method in intrawell, chaotic, and interwell oscillation modes. Furthermore, the chattering issue in conventional discontinuous controllers is eliminated with our designed continuous finite-time terminal protocols for bistable chaotic systems so as to improve the robustness of the controller and avoid its failure. Interesting findings are discussed for the varying system responses and control inputs in different oscillation modes. This work also is expected to facilitate the development of applications where bistability is found such as power or communication systems to resist the external disturbances. [ABSTRACT FROM AUTHOR]

In this paper, fast global fixed-time terminal sliding mode control for the synchronization problem of a generalized class of nonlinear perturbed chaotic systems has been investigated with the application of memristor-based oscillator in the presence of external disturbances and unmodeled dynamics. In the fixed-time control strategy, unlike conventional asymptotic or finite-time approaches, convergence time is not related to the initial conditions. In the designed global fixed-time controller, both the sliding phase and reaching phase have fixed-time convergence characteristics and consequently, via the proposed strategy, precise synchronization of the master-slave systems is accomplished within fixed convergence time. The fast fixed-time synchronization problem of the nonlinear memristor chaotic system (MCS) has been investigated. In the first stage, an in-circuit emulator (ICE) for the considered memristor is utilized in order to apply on the defined MCSs. In the next stage, according to the considered ICE, the dynamical structure of the MCS is formulated along with the fixed-time synchronization problem which is efficiently addressed via the designed controller in the presence of external disturbances and unmodeled dynamics. Finally, the strength and validity of the theoretical outcomes are confirmed through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper employs two adaptive sliding mode control (ASMC) strategies to accomplish finite-time synchronization of uncertain general fractional unified chaotic systems (UGFUCSs) when uncertainty and external disturbance exist. First, general fractional unified chaotic system (GFUCS) is developed. GFUCS may be transitioned from general Lorenz system to general Chen system, and the general kernel function could compress and extend the time domain. Furthermore, two ASMC methods are applied to finite-time synchronization of UGFUCSs, where system states arrive at sliding surfaces in finite-time. The first ASMC approach utilizes three sliding mode controllers to achieve synchronization between chaotic systems, while the second ASMC method needs just one sliding mode controller to produce synchronization between chaotic systems. Finally, the effectiveness of the proposed ASMC approaches is verified using numerical simulations. [ABSTRACT FROM AUTHOR]

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 study constructs a new 5D nonlinear hyper-chaotic system with attractive and complex behaviors. The standard behaviors of the chaotic system will also be analyzed including: Equilibrium Point (EP), Bifurcation Diagram (BD), Poincare Map (PM), Lyapunov Exponent (LE), and Kaplan-Yorke dimensional. We prove that the introduced new 5D hyper-chaotic system has complex and nonlinear behaviors. Next, the work describes Fast Terminal Sliding Mode Control (FTSMC) scheme for the control and finite-time fast synchronization of the novel 5D nonlinear hyper-chaotic system. Proof of stability for both phases has been done for the new controller with the Lyapunov stability theory. To ensure synchronization, both master-slave subsystems are perturbed by different parameter and model uncertainties. Both steps of the Sliding Mode Controller (SMC) have chaos-based fast convergence properties. Subsequently, it has been shown that the state paths of both master-slave systems can reach each other in a limited time. One of the features of the novel controller in this paper is high performance and finite-time stability of the terminal sliding surface due to derivative error and other errors. Finally, by using the MATLAB simulation, the results are confirmed for the new hyper-chaotic system. [ABSTRACT FROM AUTHOR]

In this article, the synchronization problem of hyperchaotic systems is addressed on the basis of active sliding mode control (SMC) and proportional integral (PI) SMC techniques. The stability analysis in the suggested methodologies is derived with the help of Lyapunov stability approach. In the manuscript, a comparative study presenting both above mentioned SMC approaches has been presented. Further, both the SMC techniques have been stretched to analyze secure communication for hyperchaotic systems under consideration. Switching surfaces are constructed using active SMC and PI SMC to achieve the purpose of synchronization. Between both the control techniques, PI switching surface simplifies the operation of synchronization in comparison with active control switching surface. In PI SMC, lesser number of control signals are needed to achieve the desired synchronization. The system parameters have been considered to be known. In a master–slave arrangement, the suggested controllers assure the presence of sliding motion and attain asymptotic synchronization of hyperchaotic systems. Ultimately, numerical simulations are produced to establish and authenticate the suggested controllers' effectiveness. This paper presents the effectiveness of the two control approaches designed for addressing synchronization problems along with secure communication scheme. [ABSTRACT FROM AUTHOR]

The microcontroller implementation, controls, and synchronization of a three-dimensional (3D) autonomous system with a parabolic equilibrium point are investigated in this paper. The system in question displays a reverse period doubling route hidden chaotic attractors with two different shapes. Then, the partial and total amplitude controls of the system are achieved by inserting two parameters. A microcontroller implementation is performed in order to confirm the results obtained from the numerical simulations. It is found that the results from the numerical simulations and microcontroller implementation qualitatively agree with each other. The sliding mode controllers are designed to control chaos in the system under study. With the sliding mode control method, the numerical simulations confirm that chaos can be controlled in the 3D autonomous system with a parabolic equilibrium point. In addition, two chaotic 3D autonomous systems with a parabolic equilibrium point and the same parameters are synchronized by the use of a unidirectional linear error feedback coupling scheme. Finally, an active control technique is applied to bring about chaos synchronization between two chaotic 3D autonomous systems with a parabolic equilibrium and different parameters. [ABSTRACT FROM AUTHOR]

This study reports a novel adaptive non-singular fast terminal sliding mode controller for the tracking control and synchronization of a chaotic spur gear system. The proposed novel control law attenuates the chattering phenomena of the conventional sliding mode controller. In addition, a non-singular fast terminal sliding mode surface is employed to remove the singularity problem, increase the convergence rate, and guarantee finite-time convergence. An extreme learning machine (ELM) neural network is utilized to estimate the unknown dynamics of the spur gear system and the reaching law coefficients; hence, this control scheme is a combination of the direct and indirect adaptive control. The adaptation rules of the ELM are derived based on the Lyapunov stability theorem to ensure closed-looped stability. Finally, some different numerical simulations are considered to check the validity and efficiency of the proposed control strategy compared with other control methods. [ABSTRACT FROM AUTHOR]

In order to improve the effect of dance teaching action analysis, this paper uses dance action skill feature identification method to analyze dance teaching action and combines teaching and technology to simulate dance action. Moreover, this paper conducts dynamic modeling of dance movements and analyzes the typical properties of several dynamic modeling techniques. At the same time, this paper takes the double-joint dance movement limb as the control object for comparative analysis. The comparison shows that the fractional sliding mode approaching law has better smoothing properties. In addition, this paper selects the control method combining fractional calculus and sliding mode control theory to improve the tracking speed and following effect of the double joints of dance movements. Finally, this paper studies the variance virtual spindle cross-coupling control method based on fractional-order sliding mode to further improve the synchronization accuracy of dance movement limb joints. From the experimental data, it can be seen that the application effect of dance movement skill feature recognition in dance teaching movement analysis is very good. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study premeditated the synchronization of two fractional-order chaotic systems (FOCSs) with uncertainties and external disturbances. We utilized fuzzy logic systems (FLSs) to estimate unknown nonlinearities, and implemented disturbance observers to estimate unknown bounded external disturbances. Then, a robust control term was devised to compensate for the unavoidable approximation error of the fuzzy system. In addition, a sliding mode surface was devised to construct an adaptive fuzzy sliding mode controller (AFSMC) that can guarantee that the synchronization error converges to a small neighborhood of zero. Finally, the validity of the proposed control strategy was verified via a numerical simulation.

This paper mainly proposes a new disturbance observer (DO) for a secure communication system (SCS) of the chaos-based system (CBS). First, the fractional-order (FO) Chen chaotic system is remodeled by a Takagi–Sugeno (T–S) fuzzy system with the aim of softening in calculation. Second, the robust fixed-time was designed to synchronize two nonidentical chaotic systems. Third, a new disturbance observer was proposed to compensate for the disturbance and uncertainty of the secure communication system. Fourth, the proof of the proposed method based on Lyapunov condition together with simulation are given to illustrate the correctness and effectiveness of the proposed theory. The tested disturbance on the public channel was mostly compensated by the appropriately estimated disturbance value. The states of master and slave systems (MSSs) were closed to each other in fixed-time. These factors are used to confirm that the symmetry of two chaotic systems were obtained by the proposed control methods. [ABSTRACT FROM AUTHOR]

In this study, first, a comprehensive robust control approach is proposed for projective synchronization of chaotic systems with dissimilar structures, mismatched time delays, non-identical fractional derivative orders, uncertainties, and external disturbances based on fractional-order sliding mode control strategy and fractional-order Lyapunov stability theorem. The synchronized systems are then utilized to design an analog time-varying audio cryptography system, which can secretly send voice messages through insecure communication channels. Finally, the results of numerical simulations along with security analysis demonstrate that the designed audio cryptography system has more accurate and secure results and easier practical implementation than previous audio cryptography systems. [ABSTRACT FROM AUTHOR]

Synchronization of chaotic systems is considered to be a common engineering problem. However, the proposed laws of synchronization control do not always provide robustness toward the parametric perturbations. The purpose of this article is to show the use of synergy-cybernetic approach for the construction of robust law for Arneodo chaotic systems synchronization. As the main method of design of robust control, the method of design of control with forced sliding mode of the synergetic control theory is considered. To illustrate the effectiveness of the proposed law, in this article it is compared with the classical sliding mode control and adaptive backstepping. The distinctive features of suggested robust control law are the more good compensation of parametric perturbations (better performance indexes—the root-mean-square error (RMSE), average absolute value (AVG) of error) without designing perturbation observers, the ability to exclude the chattering effect, less energy consuming and a simpler analysis of the stability of a closed-loop system. The study of the proposed control law and the change of its parameters and the place of parametric perturbation's application is carried out. It is possible to significantly reduce the synchronization error and RMSE, as well as AVG of error by reducing some parameters, but that leads to an increase in control signal amplitude. The place of application of parametric disturbances (slave or master system) has no effect on the RMSE and AVG of error. Offered approach will allow a new consideration for the design of robust control laws for chaotic systems, taking into account the ideas of directed self-organization and robust control. It can be used for synchronization other chaotic systems. [ABSTRACT FROM AUTHOR]

Synchronization of different Chaotic dynamical systems is one of the main issues in engineering which has a lot of applications in applied sciences like secure communications and cryptography. In this work, a chattering-free fractional-integral-based sliding mode control (SMC) methodology is proposed for the synchronization of different chaotic fractional-order systems with input saturation. Based on the frequency distributed model and the non-integer version of the Lyapunov stability theorem and using a new continuous function instead of sign function, a novel model-free SMC (MFSMC) method is proposed to overcome the chaotic behavior of the FOSs without any undesired chattering phenomenon. In addition, utilizing the boundedness property of the fractional-order chaotic system is caused to design the method. Then, by operating the proposed scheme on chaotic fractional-order systems, which are applied in electrical systems and secure communications, the effectiveness and applicability of the MFSMC are validated. After that, to show the real-world application, a novel encryption/decryption method for color images is introduced based on the proposed MFSMC. According to an adaption of the pre-diffusion-permutation-diffusion, the structure is adopted to improve the level of security. Furthermore, the performance and security analyses are given to confirm the superiority of the proposed encryption scheme, including histogram analysis, adjacent pixel correlation analysis, and information entropy analysis. [ABSTRACT FROM AUTHOR]

This research proposes the idea of double encryption, which is the combination of chaos synchronization of non-identical multi-fractional-order neural networks with multi-time-delays (FONNSMD) and symmetric encryption. Symmetric encryption is well known to be outstanding in speed and accuracy but less effective. Therefore, to increase the strength of data protection effectively, we combine both methods where the secret keys are generated from the third part of the neural network systems (NNS) and used only once to encrypt and decrypt the message. In addition, a fractional-order Lyapunov direct function (FOLDF) is designed and implemented in sliding mode control systems (SMCS) to maintain the convergence of approximated synchronization errors. Finally, three examples are carried out to confirm the theoretical analysis and find which synchronization is achieved. Then the result is combined with symmetric encryption to increase the security of secure communication, and a numerical simulation verifies the method's accuracy. [ABSTRACT FROM AUTHOR]

This study presents a new fractional sliding mode controller based on nonlinear fractional-order proportional integral derivative controllers to synchronize fractional-order chaotic systems with uncertainties and affected by disturbance. According to the proposed control approach, a new fractional order control law is presented which ensures robust and stable synchronization of chaotic systems in the presence of uncertainties of the master and slave systems and bounded disturbance according to Lyapunov theorem. The proposed sliding mode controller is used to synchronize two non-smooth chaotic jerk systems affected by disturbance and uncertainty. Simulation results verify effectiveness and robustness of the proposed control law. [ABSTRACT FROM AUTHOR]

This paper formulates a new fractional order (FO) integral terminal sliding mode control algorithms for the stabilization and synchronization of N-dimensional FO chaotic/hyper-chaotic systems, which are perturbed with unknown uncertainties. In order to render closed loop robustness, a novel efficient double hyperbolic functions based uncertainty estimator is developed for the estimation and mitigation of unknown uncertainties. Moreover, a double hyperbolic reaching law comprising of tangent hyperbolic and inverse sine hyperbolic functions is incorporated in the presented control techniques for the practical convergence of various chaotic system states and tracking errors to infinitesimally close to equilibrium. Examples such as FO Lu, FO Chen and FO Lorenz systems are taken to investigate robustness, finite time convergence, tracking accuracy and closed loop stability properties of the devised methodologies. Last but not least, comparative analysis is also carried out between the proposed and prior control techniques through various time domain performances such as settling time, error indices and measure of control energy. • Novel fractional order double hyperbolic integral terminal sliding mode control is developed. • Control of uncertain fractional order chaos is dealt. • Novel hyperbolic uncertainty estimator is also developed for estimation of unknown uncertainties. • Three examples are also validated along with comparative analysis with respect to prior techniques. [ABSTRACT FROM AUTHOR]

A new finding is proposed for multi-fractional order of neural networks by multi-time delay (MFNNMD) to obtain stable chaotic synchronization. Moreover, our new result proved that chaos synchronization of two MFNNMDs could occur with fixed parameters and initial conditions with the proposed control scheme called sliding mode control (SMC) based on the time-delay chaotic systems. In comparison, the fractional-order Lyapunov direct method (FLDM) is proposed and is implemented to SMC to maintain the systems' sturdiness and assure the global convergence of the error dynamics. An extensive literature survey has been conducted, and we found that many researchers focus only on fractional order of neural networks (FNNs) without delay in different systems. Furthermore, the proposed method has been tested with different multi-fractional orders and time-delay values to find the most stable MFNNMD. Finally, numerical simulations are presented by taking two MFNNMDs as an example to confirm the effectiveness of our control scheme. [ABSTRACT FROM AUTHOR]

In this paper, a sliding-mode-based controller is designed for finite-time synchronization of Memristor Chaotic Systems (MCSs). It demonstrates that the synchronization errors of the MCSs reach the designed sliding-mode surface within a finite time and the finite-time stability is achieved on the surface, which implies that the finite-time synchronization for MCSs is achieved by employing the proposed sliding-mode-based controller. Furthermore, a new image encryption algorithm is proposed and implemented based on the results of finite-time synchronization. Finally, the numerical simulation and the corresponding statistical performance analysis are presented to verify the practicability, effectiveness and superiority of the presented sliding-mode-based controller and encryption algorithm, especially their potential applications in secure communication. [ABSTRACT FROM AUTHOR]

This paper reports the finding of a new 3-D finance chaotic system with two quadratic nonlinearities and a sextic nonlinearity. We also discover interesting properties of the new finance chaotic system such as symmetry, equilibrium points, bifurcation, multistability and Lyapunov exponents. Using integral sliding mode control, we derive new results for the global chaos synchronization of a pair of new finance chaotic systems taken as master-slave systems. We illustrate all the main results of this research work using MATLAB phase plots. [ABSTRACT FROM AUTHOR]

This paper addresses the design of synergetic control (SC) for synchronizing two chaos systems represented by Takagi-Sugeno (T-S) fuzzy models. Unlike many works published, the present paper provides a new synchronization algorithm of two different hyperchaotic systems which corroborate the given analytical stability proof of the closed-loop systems. The main idea is to represent the chaos systems as an aggregated fuzzy model which compromises a set of linear models in the first place. Afterwards, the synergistic controller is applied to synchronize a nonlinear hyperchaotic (slave) system with another hyperchaotic (master) system. The proposed approach achieves hyperchaos synchronization such that it has a simple structure leading to an easy implementation. Then, theoretical analysis and numerical simulation results are compared to those obtained with a conventional sliding mode (SMC) approach clearly showing the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

Rikitake dynamo system (1958) is a famous two-disk dynamo model that is capable of executing nonlinear chaotic oscillations similar to the chaotic oscillations as revealed by palaeomagnetic study. First, we detail the Rikitake dynamo system, its signal plots and important dynamic properties. Then a circuit design using Multisim is carried out for the Rikitake dynamo system. New synchronous quasi-sliding mode control (QSMC) for Rikitake chaotic system is studied in this paper. Furthermore, the selection on switching surface and the existence of QSMC scheme is also designed in this paper. The efficiency of the QSMC scheme is illustrated with MATLAB plots. [ABSTRACT FROM AUTHOR]

The self‐adaptive terminal sliding mode synchronization of fractional‐order nonlinear chaotic systems is investigated under uncertainty and external disturbance. A novel non‐singular terminal sliding surface is proposed and proved to be stable. Based on Lyapunov stability theory, a sliding mode control law is proposed to ensure the occurrence of sliding‐mode motion. In addition, two methods of the controller and the self‐adaptive rules are used to establish the sliding mode function, and two sufficient conditions for achieving self‐adaptive terminal sliding‐mode synchronization of fractional‐order uncertain nonlinear systems are identified. The results show that designing appropriate control law and sliding‐mode surface can achieve self‐adaptive terminal sliding mode synchronization of the fractional high‐order systems with uncertainty. The effectiveness and applicability of the sliding mode control technique are validated through numerical simulation. [ABSTRACT FROM AUTHOR]

The chaotic phenomena of coronary artery systems are hazardous to health and may induce illness development. From the perspective of engineering, the potential harm can be eliminated by synchronizing chaotic coronary artery systems with a normal one. This paper investigates the chaos synchronization problem in light of the methodology of sliding mode control (SMC). Firstly, the nonlinear dynamics of coronary artery systems are presented. Since the coronary artery systems suffer from uncertainties, the technique of derivative-integral terminal SMC is employed to achieve the chaos synchronization task. The stability of such a control system is proven in the sense of Lyapunov. To verify the feasibility and effectiveness of the proposed method, some simulation results are illustrated in comparison with a benchmark.

The synchronisation of a complex chaotic network of permanent magnet synchronous motor systems has increasing practical importance in the field of electrical engineering. This article presents the control design method for the hybrid synchronization and parameter estimation of ring-connected complex chaotic network of permanent magnet synchronous motor systems. The design of the desired control law is a challenging task for control engineers due to parametric uncertainties and chaotic responses to some specific parameter values. Controllers are designed based on the adaptive integral sliding mode control to ensure hybrid synchronization and estimation of uncertain terms. To apply the adaptive ISMC, firstly the error system is converted to a unique system consisting of a nominal part along with the unknown terms which are computed adaptively. The stabilizing controller incorporating nominal control and compensator control is designed for the error system. The compensator controller, as well as the adopted laws, are designed to get the first derivative of the Lyapunov equation strictly negative. To give an illustration, the proposed technique is applied to 4-coupled motor systems yielding the convergence of error dynamics to zero, estimation of uncertain parameters, and hybrid synchronization of system states. The usefulness of the proposed method has also been tested through computer simulations and found to be valid. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of robust fuzzy sliding mode synchronization of uncertain nonlinear systems. A relevant fuzzy sliding mode control(FSMC) law is designed to force the state errors onto the specified surface. The prescribed-time boundedness (PTB) of the dynamical error is guaranteed by introducing the partitioning strategy. The chattering phenomenon, which is inherent to a conventional sliding mode control, is avoided by proper fuzzy tuning of the reaching law. The control law is deduced from the stability analysis of th closed-loop system in the sense of lyapunov. Furthermore, robustness issue is investigated and a prescribed-time property is obtained with sufficient conditions, established in terms of linear matrix inequalities (LMIs) using Lyapunov and cost functions. The results obtained show the effectiveness of the proposed control scheme and the reachability of the synchronization before the fixed time. The outcomes of this research are illustrated using computer simulations for the control problem of chaotic Chua's system, in the presence of uncertainties, which clearly reveals that FSMC is better than SMC in terms of robustness. The present proposal provides a consistent procedure to design FSMC for a general class of nonlinear systems. [ABSTRACT FROM AUTHOR]

For synchronization of a class of chaotic systems in the presence of nonvanishing uncertainties, a novel time-varying gain observer-based sliding mode control is proposed. First, a novel time-varying gain disturbance observer (TVGDO) is developed to estimate the uncertainties. Then, by using the output of TVGDO to modify sliding mode control (SMC), a new TVGDO-based SMC scheme is developed. Although the observation and control precision of conventional fixed gain disturbance observer-based control (FGDOC) for chaotic systems can be guaranteed by a high observer gain, the undesirable spike problem may be caused by the high gain if the initial values of estimate and true states are not equal. The most attractive feature of this work is that the newly proposed TVGDO can eliminate the spike problem by developing a time-varying gain scheme. Finally, the effectiveness of the proposed method is demonstrated by the numerical simulation. [ABSTRACT FROM AUTHOR]

In order to enhance the chaotic degree of cellular neural network (CNN), the memristive characteristic is combined in CNN, and a five-dimensional memristive CNN hyperchaotic system is designed. A secure communication system based on chaos synchronization is constructed by the full-dimensional state observer theory. The sliding mode control method is used to control chaos synchronization between the sending end and the receiving end and improve the robustness to the parameter uncertainties and disturbances in the system. An improved sliding mode surface is designed, and its convergence time is analyzed. Image secure communication, as an example, is given to verify the effectiveness of the proposed method. Image encryption is implemented by the hyperchaotic system, and image decryption is implemented by chaos synchronization based on the sliding mode control. Simulation experiment results show that the proposed sliding mode control method can be used to achieve the chaos synchronization of the hyperchaotic systems with parameter uncertainties and disturbances, and the proposed memristive hyperchaotic system can be applied to the secure communication based on the chaos synchronization. [ABSTRACT FROM AUTHOR]