Chaotic Systems Based Real-Time Implementation of Visual Cryptography Using LabVIEW

This research introduces an innovative control method designed for the synchronization and management of chaotic systems through the application of advanced neural network techniques. Specifically, a neural network-based sliding mode control framework is employed to enhance system stability and precision in synchronization tasks. Chaotic systems, particularly when arranged in master–slave configurations, exhibit behaviors that are highly sensitive to initial conditions and parameter variations, making them ideal candidates for the proposed approach. The core of this methodology leverages neural networks to estimate unknown nonlinear functions and dynamically adjust the control coefficients, ensuring high accuracy and adaptability in real-time. One of the key contributions of this study lies in addressing the complex issues of parametric uncertainty, external disturbances, and unmodeled dynamics that typically challenge conventional sliding mode control methods. By incorporating neural networks, the controller is equipped to effectively mitigate these uncertainties, ensuring robust performance even in the face of significant system variability. The adaptive nature of the control system allows for continuous adjustment, resulting in improved synchronization accuracy and faster convergence times. The stability and robustness of the proposed control system are rigorously proven using Lyapunov-based methods. Simulations show that synchronization of nonlinear chaotic systems occurs within 10 s, even under varying conditions. This efficiency demonstrates its practical applications in secure communications, biological systems, and power grids, marking a significant advancement in chaotic system control with broad industrial potential.

Recently, a new six-term 3-D chaotic system with an exponential nonlinearity was discovered (Sundarapandian, 2013). This novel chaotic system has two saddle focus nodes and hence they are unstable. The maximal Lyapunov exponent (MLE) for the six-term Sundarapandian chaotic system was found as 3.2827 and the Lyapunov dimension of the Sundarapandian chaotic system was found as D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> = 2.1668. Complete synchronization of chaotic systems deals with the problem of asymptotically synchronizing the states of a pair of chaotic systems called as master and slave systems with the help of controllers attached to the slave system. Complete synchronization of chaotic systems has applications in many engineering areas such as secure communications, secure data encryption, cryptosystems, etc. This paper addresses the design of active and adaptive feedback controllers for completely synchronizing the states of identical six-term Sundarapandian chaotic systems with exponential nonlinearity. Active controllers are used when the system parameters a, b and c are available for measurement and the synchronization result is established using Lyapunov stability theory. Numerical simulations using MATLAB have been shown to demonstrate the proposed active and adaptive synchronization results for the novel chaotic system discussed in this paper.

This study is concerned with the synchronization problem for a class of chaotic systems with multiple time-delays and transmitted noise. A dynamic compensator is proposed to achieve the synchronization between master and slave chaotic systems with multiple timedelays. First, the neural-network (NN) model is employed to approximate the chaotic systems with multiple time delays. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on the LDI state-space representation, an exponential stability criterion of error dynamics derived in terms of Lyapunov's direct method is proposed to ensure that the trajectories of the slave system can approach those of master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Based on the LMI, a fuzzy controller is synthesized to realize the exponential synchronization of the chaotic master-slave systems. Finally, this study provides a numerical example with simulations is given to illustrate the concepts discussed throughout this work.

Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.

SummaryRecently, the synchronization between two matching chaotic systems to provide confident communication has gained a lot of interest. Continuously, there is a necessity to produce a novel dynamical system to be used in synchronization to implement a strong security system. In this paper, a hybrid chaotic system is suggested and verified for the potential use of secure communication through chaos synchronization. The Lyapunov exponent (LE) and zero‐one (0‐1) tests have been used to verify the performance of the suggested hybrid chaotic system, while National Institute of Standard and Technology (NIST) tests have been applied to verify the randomness properties. And the synchronization has been achieved between master and slave systems by using nonlinear control laws. The simulation outcomes demonstration that the hybrid system has chaotic performance and outstanding randomness characteristic. The statistical results gained for LE test was 0.8822, and for frequency test (FT) was 0.2028, while for the run test (RT) was 0.1924. Accordingly, the suggested hybrid system can be used to evolve functional synchronization algorithms and encryption for image, video, and voice secure communication applications.

The current work presents a new concept of data transmission system based on a chaotic synchronization phenomenon. The noise immunity of the proposed communication system is also studied. This communication system can be used for secure data transmission in wireless sensor networks (WSNs) or IoT solutions. The basis of the proposed communication system is a simple Resistor-Capacitor (R-C) chaos oscillator in the transmitter and receiver parts working as master and slave systems. Two signals from the master system are used to perform communication: sin-phase for chaotic synchronization establishment and cos-phase for data transmission. In addition, the impact of difference in initial conditions of both chaos oscillators (transmitter and receiver side) on the chaotic synchronization is investigated.

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.

The main contribution of this paper is to propose a nonlinear robust controller to synchronize general chaotic systems, such that the controller does not need the information of the chaotic system’s model. Following this purpose, in this paper, two methods are proposed to synchronize general forms of chaotic systems with application in secure communication. The first method uses radial basis function neural network (RBFNN) as a controller. All the parameters of the RBFNN are derived and optimized via particle swarm optimization (PSO) algorithm and genetic algorithm (GA). In order to increase the robustness of the controller, in the second method, an integral term is added to the RBF neural network gives an integral RBFNN (IRBFNN). The coefficients of the integral term and the parameters of IRBFNN are also derived and optimized via PSO and GA. The proposed methods are applied to the famous Lorenz chaotic system for secure communication. The performance and control effort of the proposed methods are compared with the recently proposed PID controller optimized via GA. Simulation results show the superiority of the proposed methods in comparison to the recent one in improving synchronization while using smaller control effort.

Recently, many continuous-time chaotic systems were synthesized using microcontrollers and FPGAs. This requires applying mathematical discretization to convert integration into recursion. Depending on the approximation algorithms, the speed of the numerical processors, and the number of bits used to represent data, different accuracies and stabilities could be obtained. This article explores the conditions necessary to faithfully generate signals that reflect the true behavior of the chaotic systems, while maintaining the same values for their Lya-punov exponents. This is very important for chaos control and synchronization, especially for applications in secure communication that rely on digital cryptography. The Lorenz system and the Duffing oscillator are investigated to illustrate the effect of having autonomous versus non-autonomous structures. In addition, the Nosé-Hoover dynamical model is investigated to detect the relationship between agility and numerical accuracy. The obtained results prove that identical deterministic chaotic systems can behave differently, for the same set of initial conditions, depending on the discretization algorithm. This added sensitivity necessitates careful design of the mathematical models required for digital implementations of chaotic systems. The article concludes with useful recommendations for best practices in designing, synthesizing, and implementing digital chaotic systems, while commenting on the best compromise between mathematical complexity and numerical accuracy.

Audio encryption has gained popularity in a variety of fields including education, banking over the phone, military, and private audio conferences. Data encryption algorithms are necessary for processing and sending sensitive information in the context of secure speech conversations. In recent years, the importance of security in any communications system has increased. To transfer data securely, a variety of methods have been used. Chaotic system-based encryption is one of the most significant encryption methods used in the field of security. Chaos-based communication is a promising application of chaos theory and nonlinear dynamics. In this research, a chaotic algorithm for the new chaotic chameleon system was proposed, studied, and implemented. The chameleon chaotic system has been preferred to be employed because it has the property of changing from self-excited (SA) to hidden-attractor (HA) which increases the complexity of the system dynamics and gives strength to the encryption algorithm. A chaotic chameleon system is one in which, depending on the parameter values, the chaotic attractor alternates between being a hidden attractor and a self-excited attractor. This is an important feature, so it is preferable to use it in cryptography compared to other types of chaotic systems. This model was first implemented using a Field Programmable Gate Array (FPGA), which is the first time it has been implemented in practical applications. The chameleon system model was implemented using MATLAB Simulink and the Xilinx System Generator model. Self-excited, hidden, and coexisting attractors are shown in the proposed system. Vivado software was used to validate the designs, and Xilinx ZedBoard Zynq-7000 FPGA was used to implement them. The dynamic behavior of the proposed chaotic system was also studied and analysis methods, including phase portrait, bifurcation diagrams, and Lyapunov exponents. Assessing the quality of the suggested method by doing analyses of many quality measures, including correlation, differential signal-to-noise ratio (SNR), entropy, histogram analysis, and spectral density plot. The numerical analyses and simulation results demonstrate how well the suggested method performs in terms of security against different types of cryptographic assaults.

Chaos science is also used in the fields of medicine, biology and finance besides in the engineering fields such as communications, electronics and computer. Up till today, many different chaotic systems have been introduced in the literature in order to be used in these fields. The majority of these systems have usually been examined numerically and only some of them have electronic circuit design. The chaotic systems must be able to be done electronically especially in the fields such as secure communication, encryption, etc. In 1994 were found 19 attractor systems that were simple-structured but producing complex chaotic signals and named A to S by Sprott. In this study electronic circuit design of Sprott H chaotic system with the positive (non-inverting) second generation current conveyor with high gain and high bandwidth were performed in Orcad-PSPICE program. Numerical analysis results of Sprott H chaotic system and the designed electronic circuit outputs were found to be the same. The system can be used secure communication and encryption applications of which electronic circuit were designed.

Chaos synchronization is a phenomenon that occurs when a chaotic system drives another chaotic system. If a certain chaotic system is called the master system and another chaotic system is called the slave system, then anti-synchronization is said to occur when the state vectors of the master and slave systems have the same amplitude but opposite signs. This paper derives an important result for the anti-synchronization of identical chaotic systems using sliding mode control. This main result has been established using Lyapunov stability theory. In robust control systems, the sliding mode control (SMC) is often preferred in view of its inherent advantages such as easy realization, fast response, good transient performance and also insensitivity to parameter uncertainties and external disturbances. As an application of this general result, this paper solves the anti-synchronization problem for identical Wang-Chen chaotic systems (2012) via sliding mode control. Numerical simulations using MATLAB have been presented in detail to validate the sliding controller design for achieving anti-synchronization of identical Wang-Chen chaotic systems.

In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master‐slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.

The variable-order fractional (VOF) chaotic systems offer a promising solution for applications in secure communication due to their unique properties. This paper addresses the synchronisation problem in secure communication for these systems, which have uncertainties and external disturbances with unknown bounds. According to the variable-order fractional type Mittag-Leffler stability theorem, a fractional-order derivative is applied to a sliding surface, and suitable adaptive laws are devised to address uncertainties and disturbances. A variable-order fractional control strategy and a new criterion are developed to ensure the synchronisation error systems achieve asymptotic stability in finite time, for which the upper limit can be obtained. Simulation outcomes demonstrate the efficacy of the proposed synchronisation strategy in secure communication scenarios.

This paper reports a new 3-dimensional autonomous chaotic system with four nonlinearities. The system is studied with respect to its numerical solutions in phase space, including sensitive dependence on initial conditions, equilibrium points, bifurcation, and maximal Lyapunov exponent. It is shown that the system is dissipative and has a fractional Lyapunov dimension. Besides, a basin of attraction is determined by the Newton–Raphson’s method. To show its practicality, the new system is implemented by means of an analog electronic circuit. Aperiodicity of the experimental signal is verified by means of an improved power spectral density estimator, viz., the Welch’s method. Also, the correlation dimension is estimated from the experimental time series with the result confirming that the responses are deterministic chaos. Finally, an electronic design of a secure communication application is carried out, wherein a nontrivial square wave is modulated by a master chaotic signal. The modulated signal is subsequently recovered by a slave system, and the fast convergence to zero of the information recovery error substantiates the effectiveness of the design.