Synchronization Of Chaotic Systems Research Articles

Enhancing network security with hybrid feedback systems in chaotic optical communication

This paper presents a pioneering approach to bolstering network security and privacy by implementing chaotic optical communication with a hybrid optical feedback system (HOFS). The current baseline methods in network security are often less feasible for hybrid feedback systems, including limited robustness, compromised security, and synchronization challenges. Therefore, this paper proposes a hybrid approach to address these shortcomings by integrating the HOFS into chaotic optical communication systems (HOFS-COCS) to overcome the baseline challenges. This paper aims to improve network security while significantly maintaining efficient communication channels. Moreover, We designed two algorithms, one for chaotic maps generation and another for text encryption and decryption, to improve security in the hybrid feedback system. Our findings demonstrate through rigorous experimentation and analysis that the proposed (HOFS-COCS) method significantly improves network security by enabling reliable chaos generation, synchronization, and secure message transmission in chaotic optical communication systems. This research represents a significant advancement towards enhanced secrecy and synchronization in chaotic optical communication systems, promising a paradigm shift in network security protocols.

The influence of equilibrium points and initial values on multistability of a multi-scroll chaotic system and predefined-time synchronization

Abstract In order to explore the effect of the initial value on the symmetry of the coexisting attractor, a novel multi-scroll chaotic system is designed in this paper. The system is proved to be chaotic by analysing the phase diagram, Lyapunov exponential spectrum and dissipativity of the system. Then the equilibrium point of the system is investigated and it is found that the system has four symmetric saddle focus of index 2. By analysing the dynamical behaviour of the system, it is found that the system has a special kind of multistability. Combining the properties of the orbits near the saddle focus of indicator 2, the reason for this special multistability is explained, and the effect of the positional relationship between the initial value and the saddle focus on the symmetry of the coexisting attractors is illustrated, which provides a new way of thinking to analyse the symmetric coexistence of chaotic systems. In order to verify the feasibility and application value of the system, simulation circuits are designed and predefined-time synchronization between systems of different dimensions is achieved.

A novel adaptive parameter zeroing neural network for the synchronization of complex chaotic systems and its field programmable gate array implementation

This article proposes a novel adaptive-parameter zeroing neural network (NAP-ZNN) to control the synchronization of complex chaotic systems. Different from previous zeroing neural networks (ZNNs), the NAP-ZNN model incorporates adaptive-parameter, a unique blend of time-varying convergence factor and fuzzy control parameter, which is adjusted continuously according to the real-time synchronizing error, offering greater flexibility. The NAP-ZNN model aims to address the time-varying problem in complex-valued domain, which is scarcely explored, it rapidly impels two complex chaotic systems to synchronize within predetermined time and effectively mitigates noise interference. Moreover, the upper bound of the convergence time is theoretically calculated in noiseless environments, and the disturbance-resistant property is demonstrated under various noisy disturbances. The control performance of NAP-ZNN model has been separately compared to other general ZNNs (NAP-ZNN synchronizes at 0.097 s while three general ZNNs spend 0.43 s, 0.78 s and 0.84 s, and only NAP-ZNN complete synchronization within 0.1 s under noisy interferences while general ZNNs fail) and the traditional adaptive control method through two synchronization simulation (RMSE of NAP-ZNN under sinusoidal noise is 3.165 × 10-3 while traditional is 3.383 at t = 1 s). The numerical outcomes clearly illustrate the superior performance of the NAP-ZNN model in comparison to other synchronization strategies. The hardware implementation of the NAP-ZNN model has been successfully realized through the Field Programmable Gate Array (FPGA), and the chaos synchronization process has been vividly captured via an oscilloscope, further reinforcing the practicality and effectiveness of the NAP-ZNN model.

Multi-frequency weak signal detection based on Liu-like chaotic synchronization system and its hardware circuit implementation

Considering the shortcomings of traditional chaotic systems in weak signal detection methods, such as the high threshold sensitivity requirement and the narrow detection frequency domain. This study proposes a novel three-dimensional chaotic synchronization system, and the dynamical of the system are exhaustively characterized using equilibrium points, phase diagrams, Lyapunov exponential spectra, and bifurcation diagrams. This method involves weak signal detection by means of chaotic synchronization control. Synchronization of a chaotic system using a backstepping synchronization method is used to detect weak signals by analyzing the synchronization error after the introduction of weak signals in a strong noise background. The chaotic system is implemented by hardware circuits, and the simulation of chaotic synchronization control and detection of weak signals from the perspective of circuits is carried out by circuit simulation software. Additionally, the frequency range within which the system is capable of weak signal detection is tested through extensive simulation experiments. Finally, multi-frequency signals detection experiments are performed. The experimental results demonstrate that the system can accurately detect the frequency of weak signals address the limitations of narrow-band detection and multi-frequency signal detection is possible. Meanwhile, the circuit structure proposed in this paper is simple and has some value for engineering applications.

Specified time dual-group synchronization of uncertain complex chaotic systems

Aiming at the specified time dual-group synchronization problem of multi-wing complex chaotic systems containing uncertain terms and external disturbances, a new specified-time sliding mode control scheme is proposed, which directly synchronizes the complex chaotic system without separating the real and imaginary parts of the complex chaotic system. First, a new specified time stability criterion is used to construct the integral sliding mode surface of the synchronous error system to ensure stable sliding motion within the specified time. Subsequently, a proximity controller is designed to drive the error system to reach and remain on the sliding surface within another specified time, thereby achieving specified-time synchronization. In order to realize the proposed stability concept, this paper introduces a new sliding surface and defines the corresponding control law and adaptive rate. The effectiveness of this scheme is proved through Lyapunov stability theory and specified time stability theory. Numerical simulation results show that the scheme has strong robustness to uncertainties and external disturbances, and the controller is not affected by internal uncertainties and external disturbances. Compared to other stabilization time control schemes, this scheme has a shorter synchronization time. In general, this study introduces complex variables and adopts a scheme in which sliding mode surface parameters and controller parameters can be preset to simultaneously achieve dual-group synchronization of two groups of complex chaotic systems within the complex domain. This study offers greater flexibility, presenting novel ideas and approaches for the synchronization control of complex systems. It holds significant theoretical and practical value, providing valuable references and insights for research and applications in related fields.

State Observer Synchronization of Three-dimensional Chaotic Oscillatory Systems Based on DNA Strand Displacement.

Currently, DNA strand displacement (DSD) as the theoretical basis of DNA chemical reaction networks (CRNs) has promoted the development of chaotic synchronization technique. This paper introduces the synchronization technology of two isomorphic three-dimensional chaotic systems based on DNA strand displacement under state observer. By studying the theoretical knowledge of DNA molecules, multiple DSD reactions are used to construct three-dimensional chaotic system. Based on two isomorphic chaotic systems, the linear transformation system and the state observer system are designed according to the theory of state observer construction. In addition, in order to realize the synchronization of chaotic systems, a coupling controller is designed between the drive system and the linear transformation system, and a soft variable-structure controller is designed between the state observer system and the response system. Through multiple DSD reactions, the chemical reaction networks of four chaotic systems and two controllers are constructed, and they are cascaded to realize the synchronization of two isomorphic three-dimensional chaotic systems. Numerical simulations verify the effectiveness and robustness of the scheme. Our work will extend and provide a reference for new methods to achieve synchronization of chaotic systems using DSD.

Synchronization of Bidirectionally Coupled Fractional-Order Chaotic Systems with Unknown Time-Varying Parameter Disturbance in Different Dimensions

In this article, the synchronization of bidirectionally coupled fractional-order chaotic systems with unknown time-varying parameter disturbance in different dimensions is investigated. The scale matrices are designed to address the problem of the synchronization for fractional-order chaotic systems across two different dimensions. Congelation of variables is used to deal with the unknown time-varying parameter disturbance. Based on Lyapunov’s stability theorem, the synchronization controllers in different dimensions are obtained. At the same time, adaptive laws of the unknown disturbance can be designed. Benefiting from the proposed methods, we verify all the synchronization errors can converge to zero as time approaches infinity, regardless of whether in n-D or m-D synchronization, simultaneously ensuring that both control and estimation signals are bounded. Finally, simulation studies based on fractional-order financial systems are carried out to validate the effectiveness of the proposed synchronization method.

Function matrix projective synchronization for disturbed fractional laser chaotic systems and image encryption

Fractional laser chaotic systems can exhibit more complex dynamical behavior, so its projective synchronization and applications to image encryption have been widely investigated in recent years. This work devotes to realize its function matrix projective synchronization, whose projective scale factor is a function matrix varying with time t, and applies the function matrix projective synchronization to the color image encryption. First, two different fractional laser chaotic systems with model uncertainty and external disturbance are constructed and the function matrix projective synchronization is defined. Second, the fractional sliding mode surface and the sliding mode controller are designed to achieve the function matrix projective synchronization. And, the synchronization analysis is confirmed by numerical simulation. Finally, by Zigzag transformation and DNA coding, the function matrix projective synchronization is applied to the color image encryption. And the comparison results shows that an excellent encryption scheme can be designed by the complex projection factor. This work not only extends the concept of the projective synchronization, but also provides an effective method for the image encryption.

Adaptive fixed-time difference synchronization for different classes of chaotic dynamical systems

This article examines adaptive fixed-time difference synchronization for various classes of chaotic dynamical systems. The adaptive fixed-time control technique has been used in this article to investigate the difference synchronization for the Sprott chaotic system, both with and without delay. The fixed settling time (T) has been estimated successfully. It is also shown that the trajectories of error states approach to the origin within a fixed time (T). The theoretical analysis is validated by simulating Sprott chaotic systems both with and without delay. On the other hand, various nonlinear chaotic systems are explored for difference synchronization in discrete chaotic systems. Several chaotic maps, including Tinkerbell, Henon, and Hitzl-Zele, have been used to achieve synchronization in these discrete systems. The numerical results are presented graphically, verifying the theoretical outcomes of difference synchronization for various classes of chaotic dynamical systems.

A new fixed-time sliding mode control scheme for synchronization of chaotic systems

Chaotic synchronization is crucial in the field of secure communication, and fixed-time synchronization has realistic application prospects and demands. Aiming at the traditional sliding mode synchronization control method with chattering problem, based on the Lyapunov stability theory and incorporating the continuous time fixed time stability theorem, this paper proposed a new fixed-time sliding mode control scheme for synchronization of chaotic systems. The traditional finite-time sliding mode synchronization is compared with the proposed fixed-time sliding mode synchronization scheme and the results are discussed. The efficacy of the controller is validated using MATLAB simulations, which eliminates the chatter problem in the traditional sliding mode synchronization scheme and has the advantage of short synchronization time. In addition, the parameters of the controller can be set flexibly, which is an advantage of the fixed-time synchronous control scheme.

A Fixed-Time Noise-Tolerance ZNN Model for Time-Variant Inequality-Constrained Quaternion Matrix Least-Squares Problem.

Presently, numerical algorithms for solving quaternion least-squares problems have been intensively studied and utilized in various disciplines. However, they are unsuitable for solving the corresponding time-variant problems, and thus few studies have explored the solution to the time-variant inequality-constrained quaternion matrix least-squares problem (TVIQLS). To do so, this article designs a fixed-time noise-tolerance zeroing neural network (FTNTZNN) model to determine the solution of the TVIQLS in a complex environment by exploiting the integral structure and the improved activation function (AF). The FTNTZNN model is immune to the effects of initial values and external noise, which is much superior to the conventional zeroing neural network (CZNN) models. Besides, detailed theoretical derivations about the global stability, the fixed-time (FXT) convergence, and the robustness of the FTNTZNN model are provided. Simulation results indicate that the FTNTZNN model has a shorter convergence time and superior robustness compared to other zeroing neural network (ZNN) models activated by ordinary AFs. At last, the construction method of the FTNTZNN model is successfully applied to the synchronization of Lorenz chaotic systems (LCSs), which shows the practical application value of the FTNTZNN model.

Adaptive fuzzy quantized prescribed performance synchronization of uncertain non-strict feedback chaotic systems with time-varying actuator failure

This paper addresses an adaptive fuzzy prescribed performance synchronization for a class of uncertain non-strict feedback chaotic systems subject to input quantization and time-varying actuator faults. The proposed approach utilizes fuzzy logic systems to estimate uncertainties. In addition, multiplicative and additive faults are considered simultaneously, which may occur either separately or simultaneously. To address the challenge, based on the backstepping scheme and a filter, an intermediate controller is conducted to compensate for the interference between actuator faults and quantification, in which a damping term and a positive time-varying function are introduced. Moreover, treating the error system as a constrained system, a simplified nonlinear mapping is employed to achieve asymmetric prescribed performance synchronization. Unlike traditional methods that rely on barrier Lyapunov functions and switch functions, the proposed approach eliminates the need for a switch function and extends the action scope to cover all synchronization errors. The analysis demonstrates that even if actuator faults and input quantization coexist, all signals in the closed-loop system remain bounded, and synchronization errors remain within the prescribed performance range. Finally, synchronization simulations are conducted on a nonlinear gyroscope system and a Non-autonomous chaotic Micro-Electro-Mechanical-System to reveal the validity of the proposed scheme.

Chaos Control and Synchronization of a New Fractional Laser Chaotic System

In this article, we introduce a new fractional laser chaotic system derived from the Lorenz–Haken equations. We investigate the complex dynamics of the proposed system consisting chaos, stability, control and synchronization of chaos. Moreover, we numerically reveal the nonlinear dynamics of the fractional laser chaotic system through the phase portraits, time histories and bifurcation diagrams. Also, we indicate the chaotic behaviors of the system by means of Lyapunov exponents, bifurcation diagrams versus all parameters along the state variables, phase portraits and time histories with different trajectories and initial conditions. The necessary conditions to eliminate the chaotic vibration of the system are obtained via the feedback control procedure. Meanwhile, a synchronization mechanism based on the feedback control technique is achieved for coupled fractional laser chaotic systems. Furthermore, we show that the fractional derivative order is very effective on reducing the irregular and chaotic behaviors of the system.

A noise‐tolerant fuzzy‐type zeroing neural network for robust synchronization of chaotic systems

SummaryAs a significant research issue in control and science field, chaos synchronization has attracted wide attention in recent years. However, it is difficult for traditional control methods to realize synchronization in predefined time and resist external interference effectively. Inspired by the excellent performance of zeroing neural network (ZNN) and the wide application of fuzzy logic system (FLS), a noise‐tolerant fuzzy‐type zeroing neural network (NTFTZNN) with fuzzy time‐varying convergent parameter is proposed for the synchronization of chaotic systems in this paper. Notably the fuzzy parameter generated from FLS combined with traditional convergent parameter embedded into this NTFTZNN can adjust the convergence rate according to the synchronization errors. For the sake of emphasizing the advantages of NTFTZNN model, other three sets of contrast models (FTZNN, VPZNN, and PTZNN) are constructed for the purpose of comparison. Besides, the predefined‐time convergence and noise‐tolerant ability of NTFTZNN model are distinctly demonstrated by detailed theoretical analysis. Furthermore, synchronization simulation experiments including two chaotic systems with different dimensions are provided to verify the related mathematical theories. Finally, the schematic of NTFTZNN model for chaos synchronization is accomplished completely through Simulink, further accentuating its effectiveness and potentials in practical applications.

Investigation of a high-performance control algorithm for a unified chaotic system synchronization control based on parameter adaptive method

With the rapid development of computer technology, parameter adaptive control methods are becoming more and more widely used in nonlinear systems. However, there are still many problems with synchronous controllers with multiple inputs and a single output, uncertainty, and dynamic characteristics. This paper analyzed a synchronization control strategy of uncoupled nonlinear systems based on parameter dynamic factors to adjust the performance of the synchronization controller, and briefly introduced the manifestations of chaotic motion. The characteristics and differences of continuous feedback control methods and transmission and transfer control methods were pointed out. Simple, effective, stable, and feasible synchronous control was analyzed using parameter-adaptive control theory. By analyzing the non-linear relationships between various models at different orders, the fuzzy distribution of the second-order mean and their independent and uncorrelated matrices were obtained, and their corresponding law formulas were established to solve the functional expression between the corresponding state variables and the dynamic characteristics of the system. The error risk test, computational complexity test, synchronization performance score test, and chaos system control effect score test were carried out on the control algorithms of traditional chaos system synchronization methods and chaos system synchronization methods based on parameter adaptive methods. Parameter adaptive methods were found to effectively reduce the error risk of high-performance control algorithms for synchronization of the unified chaos system. The complexity of the calculation process was simplified and the complexity score of the calculation process was reduced by 0.6. The application of parameter adaptive methods could effectively improve the synchronization performance of control algorithms, and the control effectiveness rating of control algorithms was improved. The experimental test results proved the effectiveness of control algorithms, which greatly enriched the field of modern control applications and also drove the vigorous development of nonlinear dynamics research, thus making significant progress in chaos application research.

Fixed-time Synergetic Control for Synchronization of Fractional-order Chaotic Systems

In this paper, a fixed-time synergetic control is proposed for the synchronization of fractional-order chaotic systems. It is similar to the sliding mode approach but without chattering and achieves exact convergence of the macro-variable. Synergetic control is a robust approach that does not require linearization and is suitable for real-time implementation since it does not require a discontinuous term in its control law. The Lyapunov framework is used to ensure the convergence of the controlled system. Computer simulations are performed to illustrate the effectiveness of the proposed method.

Generalized Synchronization of Different Chaotic System via Linear Mapping

Generalized Synchronization of Different Chaotic System via Linear Mapping

Enhancing the trustworthiness of chaos and synchronization of chaotic satellite model: a practice of discrete fractional-order approaches

Accurate development of satellite maneuvers necessitates a broad orbital dynamical system and efficient nonlinear control techniques. For achieving the intended formation, a framework of a discrete fractional difference satellite model is constructed by the use of commensurate and non-commensurate orders for the control and synchronization of fractional-order chaotic satellite system. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as Lyapunov exponent research, phase images and bifurcation schematics. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of satellite systems in order to provide justification for the structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the satellite system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample entropy evaluation is employed in the research to determine complexities and endorse the existence of chaos. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the satellite chaotic model is an intriguing and crucial subject for research.

Extreme Homogeneous and Heterogeneous Multistability in a Novel 5D Memristor-Based Chaotic System with Hidden Attractors

This paper proposes a novel five-dimensional (5D) memristor-based chaotic system by introducing a flux-controlled memristor into a 3D chaotic system with two stable equilibrium points, and increases the dimensionality utilizing the state feedback control method. The newly proposed memristor-based chaotic system has line equilibrium points, so the corresponding attractor belongs to a hidden attractor. By using typical nonlinear analysis tools, the complicated dynamical behaviors of the new system are explored, which reveals many interesting phenomena, including extreme homogeneous and heterogeneous multistabilities, hidden transient state and state transition behavior, and offset-boosting control. Meanwhile, the unstable periodic orbits embedded in the hidden chaotic attractor were calculated by the variational method, and the corresponding pruning rules were summarized. Furthermore, the analog and DSP circuit implementation illustrates the flexibility of the proposed memristic system. Finally, the active synchronization of the memristor-based chaotic system was investigated, demonstrating the important engineering application values of the new system.

A new predictive intelligent controller and path planning for mobile robots

This paper studies the synchronization and control of chaotic systems, and a new chaotic-based path is designed for Mobile robots (MRs). The chaotic systems are used to design an unpredictable path for a class of patrol MRs. To enhance security, multiple chaotic systems with a chaotic switching mechanism are introduced for path planning. The main challenge is that the dynamics of MRs are entirely unknown. The physical dynamics are not reliable in practice, because many parameters in MR dynamics are changed due to unknown environmental conditions such as noisy sensors, time delays, friction, and non-ideal actuators. Also, the chaotic switching of reference signals between chaotic signals imposes a high dynamic perturbation. So, a powerful fractional-order predictive controller on the basis of type-3 (T3) fuzzy-logic systems (FLSs) is developed. The estimation and prediction errors of T3-FLSs are compensated by a designed parallel compensator. T3-FLSs are online tuned such that stability is ensured, and the defined cost function for prediction controller is minimized. The suggested scheme is implemented on a real-world MR, and the results demonstrate the febrility and the accuracy. Also, in several simulations, the efficacy of the designed controller is examined. The simulation and experimental results show that the accuracy is improved more than 70% in comparison with conventional predictive controllers under noisy signals and uncertain dynamics.