Complex Chaotic Systems Research Articles

The global attractive sets and synchronization of a fractional-order complex dynamical system

<abstract><p>This paper presents a chaotic complex system with a fractional-order derivative. The dynamical behaviors of the proposed system such as phase portraits, bifurcation diagrams, and the Lyapunov exponents are investigated. The main contribution of this effort is an implementation of Mittag-Leffler boundedness. The global attractive sets (GASs) and positive invariant sets (PISs) for the fractional chaotic complex system are derived based on the Lyapunov stability theory and the Mittag-Leffler function. Furthermore, an effective control strategy is also designed to achieve the global synchronization of two fractional chaotic systems. The corresponding boundedness is numerically verified to show the effectiveness of the theoretical analysis.</p></abstract>

Impulsive Synchronization Control Mechanism for Fractional-Order Complex-Valued Reaction-Diffusion Systems With Sampled-Data Control: Its Application to Image Encryption

This article is devoted to gain a better understanding of the synchronization control mechanism in networked, complex-valued reaction-diffusion systems via an impulsive and sampled-data controller. Different from the traditional control methods with hybrid mechanism, an impulsive and sampled-data control scheme is proposed for fractional-order complex-valued reaction-diffusion neural networks (FRDCVNNs). By utilizing Lyapunov functional and inequality techniques, finite-time Mittag-Leffler synchronization criteria via an impulsive and sampled-data controller are established and presented as linear matrix inequalities (LMIs), which can ensure the finite-time synchronization of error system containing the drive and response dynamics. In addition, synchronization control mechanism on the considered system via impulsive actuator saturation and sampled-data control are applied. Simulation examples are provided to verify the efficacy of the proposed synchronization criterion and the results of practical application to image encryption scheme based on the chaotic complex system is presented. Furthermore, the proposed cryptosystem have obvious advantages of large key space and high security.

Different Kinds of Modulus–Modulus Synchronization for Chaotic Complex Systems and Their Applications

Different Kinds of Modulus–Modulus Synchronization for Chaotic Complex Systems and Their Applications

Dynamic Analysis and Coupling Synchronization Control of A Class of Four-dimensional Chaotic Systems

In this paper, for a class of four-dimensional complex chaotic systems, the stability of the equilibrium point of the system and the dissipation of the system are analyzed. Secondly, the complex chaotic attractors of the system are studied. At the same time, the chaotic behavior of the system is quantitatively analyzed by "0-1" test. Conclusion it is proved that the system has complex chaotic characteristics. Finally, through the establishment of the theory of coupling synchronization control for the four-dimensional chaotic system, the numerical analysis shows that the system can achieve synchronization control in a short time.

SIGNAL PROCESSING AND CYBERSECURITY IN SOME CHAOTIC OPTICAL COMMUNICTAION SYSTEMS

A chaos –geometric approach to investigation of complex chaotic dynamical systems is applied to an analysis, modeling and processing the time series of emission intensities of chaotic transmitter/receiver systems (two unidirectionally coupled semiconductor laser systems in the all-optical scheme) suited for encoding at rates of GBit/s. the problem of a signal processing is directly connected with the corresponding cybersecurity in some optical chaos communictaion systems. The estimated values for the dynamic and topologic invariants such as the correlation and Kaplan-York dimensions, Lyapunov indicators, Kolmogorov entropy etc for investigated chaotic signal time series of two unidirectionally coupled semiconductor laser systems in the all-optical scheme.

Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for nth-Order Perturbed Nonlinear Systems

In this study, an adaptive nonsingular finite time control technique based on a barrier function terminal sliding mode controller is proposed for the robust stability of nth-order nonlinear dynamic systems with external disturbances. The barrier function adaptive terminal sliding mode control makes the convergence of tracking errors to a region near zero in the finite time. Moreover, the suggested method does not need the information of upper bounds of perturbations which are commonly applied to the sliding mode control procedure. The Lyapunov stability analysis proves that the errors converge to the determined region. Last of all, simulations and experimental results on a complex new chaotic system with a high Kaplan–Yorke dimension are provided to confirm the efficacy of the planned method. The results demonstrate that the suggested controller has a stronger tracking than the adaptive controller and the results are satisfactory with the application of the controller based on chaotic synchronization on the chaotic system.

A New Synchronization Method for Time-Delay Fractional Complex Chaotic System and Its Application

This paper proposes a class of time-delay fractional complex Lu¨ system and utilizes the adomian decomposition algorithm to study the dynamics of the system. Firstly, the time chaotic attractor, coexistence attractor and parameter space are studied. The bifurcation diagram and complexity are used to analyze the dynamic characteristics of the system. Secondly, the definition of modified fractional projective difference function synchronization (MFPDFS) is introduced. The corresponding synchronous controller is designed to realize the MFPDFS of the time-delay fractional complex Lu¨ system. Thirdly, based on the background of wireless speech communication system (WSCs), the MFPDFS controller is used to realize the secure speech transmission. Finally, the effectiveness of the controller is verified by numerical simulation. The signal-noise ratio (SNR) analysis of speech transmission is given. The performance of secure communication is verified by numerical simulation.

FPGA REALIZATION OF COMPLEX LOGISTIC MAP FRACTAL BEHAVIOR

This paper studies the capability of digital architecture to mimic fractal behavior. As chaotic attractors realized digitally had opened many tracks, digital designs mimicking fractals may ultimately achieve the same. This study is based on a complex single-dimensional discrete chaotic system known as the generalized positive logistic map. The fractals realized from this system are linked to the results of the mathematical analysis to understand the fractal behavior with different variations. A digital hardware architecture manifesting the fractal behavior is achieved on FPGA, showing a fractal entity experimentally. With this digital realization, it is hoped that fractals can follow the example of chaotic attractors digital applications.

Predicting the chaos and solution bounds in a complex dynamical system

The competitive modes for a nonlinear chaotic complex system are studied in this paper. In hyperchaotic, chaotic, and periodic cases, we examined competitive modes that are a tool for detecting chaos in a system. Also, using an analytical method and Lagrange optimization, we were able to calculate the ultimate bound of the nonlinear chaotic complex systems. We have presented is simpler and more accurate than other methods that implicitly calculate the ultimate bound. The estimation of the explicit ultimate bound can be used to study chaos control and chaos synchronization. Numerical simulations illustrate the analytical results.

An Image Encryption Algorithm Using Logistic Map with Plaintext-Related Parameter Values.

This paper deals with a plaintext-related image encryption algorithm that modifies the parameter values used by the logistic map according to plain image pixel intensities. The parameter values are altered in a row-wise manner, which enables the usage of the same procedure also during the decryption. Furthermore, the parameter modification technique takes into account knowledge about the logistic map, its fixed points and possible periodic cycles. Since the resulting interval of parameter values achieves high positive values of Lyapunov exponents, the chaotic behavior of the logistic map should be most pronounced. These assumptions are verified by a set of experiments and the obtained numerical values are compared with those reported in relevant papers. It is found that the proposed design that uses a simpler, but well-studied, chaotic map with mitigated issues obtains results comparable with algorithms that use more complex chaotic systems. Moreover, the proposed solution is much faster than other approaches with a similar purpose.

Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique.

In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system.

Complex compound-combination multi switching anti-synchronization of fractional-order complex chaotic systems and integer-order complex chaotic systems

Based on three fractional-order complex chaotic systems and two integer-order complex chaotic systems, we propose a novel synchronization scenario of complex compound-combination multi-switching anti-synchronization (CCCMSAS), which is the first of this kind. The CCCMSAS states are completed between three leader and two follower systems by adopting the nonlinear control method and choosing suitable Lyapunov function on the basis of the complex space. Furthermore, different switches and leader–follower systems of different dimensions are selected as the two examples to show the validity and maneuverability of the proposed scheme.

New Fractional Order Chaotic System: Analysis, Synchronization, and it’s Application

In this paper, a new nonlinear dynamic system, new three-dimensional fractional order complex chaotic system, is presented. This new system can display hidden chaotic attractors or self-excited chaotic attractors. The Dynamic behaviors of this system have been considered analytically and numerically. Different means including the equilibria, chaotic attractor phase portraits, the Lyapunov exponent, and the bifurcation diagrams are investigated to show the chaos behavior in this new system. Also, a synchronization technique between two identical new systems has been developed in master- slave configuration. The two identical systems are synchronized quickly. Furthermore, the master-slave synchronization is applied in secure communication scheme based on chaotic masking technique. In the application, it is noted that the message is encrypted and transmitted with high security in the transmitter side, in the other hand the original message has been discovered with high accuracy in the receiver side. The corresponding numerical simulation results proved the efficacy and practicability of the developed synchronization technique and its application

Exponential synchronization of fractional-order complex chaotic systems and its application

In this article, exponential synchronization between fractional order chaotic systems has been studied by using exponential stability theorem. The stability analysis has been done with help of an existing lemma, which is given for Lyapunov function for fractional order system. The fractional order complex chaotic systems viz., Lorenz and Lu systems are considered to illustrate the exponential synchronization. The numerical simulation results are presented through graphical plots to verify the effectiveness and reliability of exponential synchronization. The application in communication through digital cryptography is also discussed between the sender (transmitter) and receiver using the exponential synchronization. A well secured key system of a message is obtained in a systematic way.

Configuration analysis of influencing factors of operating efficiency based on fsQCA: evidence from China’s property insurance industry

PurposeBased on the perspective of complexity theory, the operation process of property insurance companies can be regarded as a complex dynamic nonlinear chaotic system. This paper aims to measure the operating efficiency of 29 Chinese domestic property and casualty (P&C) companies and 18 foreign-invested P&C companies from 2011 to 2017 and outline the path to achieving high-quality development.Design/methodology/approachThe data were obtained from the Chinese Insurance Yearbook and China Statistical Yearbook 2012–2018. The data envelopment analysis method was used to calculate the technical efficiency of property insurance companies and fuzzy set qualitative comparative analysis is used for configuration analysis of determinants affecting technical efficiency.FindingsThis paper founds the average technical efficiency of Chinese domestic P&C insurance companies was 0.914 and that of foreign-invested P&C insurance companies was 0.895. The average total factor productivity of Chinese domestic P&C insurance companies was 1.058 and that of foreign-invested P&C insurance companies was 1.051. There were three modes to improve the company’s technical efficiency, with high loss ratio and low reinsurance ratio, poor employee education and higher leverage ratio and high leverage ratio and low reinsurance ratio as the core conditions.Originality/valueThis study puts forward four applicable, targeted and proven ways to improve the technical efficiency of China’s P&C insurance industry. These configurations were verified by the cases of existing property insurance companies, which can provide practical references for the insurance industry.

Security Analysis of a Color Image Encryption Algorithm Using a Fractional-Order Chaos.

Fractional-order chaos has complex dynamic behavior characteristics, so its application in secure communication has attracted much attention. Compared with the design of fractional-order chaos-based cipher, there are fewer researches on security analysis. This paper conducts a comprehensive security analysis of a color image encryption algorithm using a fractional-order hyperchaotic system (CIEA-FOHS). Experimental simulation based on excellent numerical statistical results supported that CIEA-FOHS is cryptographically secure. Yet, from the perspective of cryptanalysis, this paper found that CIEA-FOHS can be broken by a chosen-plaintext attack method owing to its some inherent security defects. Firstly, the diffusion part can be eliminated by choosing some special images with all the same pixel values. Secondly, the permutation-only part can be deciphered by some chosen plain images and the corresponding cipher images. Finally, using the equivalent diffusion and permutation keys obtained in the previous two steps, the original plain image can be recovered from a target cipher image. Theoretical analysis and experimental simulations show that the attack method is both effective and efficient. To enhance the security, some suggestions for improvement are given. The reported results would help the designers of chaotic cryptography pay more attention to the gap of complex chaotic system and secure cryptosystem.

A new hyperchaotic complex system and its synchronization realization

In this paper, we propose a new hyperchaotic complex system and systematically study its basic dynamic characteristics such as dissipation, Lyapunov exponent, attractor, parameter changes, and cross-section. The system is based on the complex Lorenz chaotic system, and the chaotic system has higher dimensionality and more parameters than complex Lorenz system. We provide a general method for constructing complex chaotic systems. We use the state linear feedback method to realize the synchronization control of the chaotic system as the driving system and the response system and simulate all of the systems by Simulink. The chaotic system and its synchronization simulation are simulated by Simulink to verify their hardware feasibility.

Synchronization between Integer and Fractional Chaotic Systems Via. Tracking Control and Non Linear Control With Application

In this paper the synchronization between complex fractional order chaotic system and integer order hyper chaotic system has been investigated. Due to increased complexity and presence of additional variables, it seems to be very interesting and can be associated with real life problems. Based on the idea of tracking control and non linear control, we have designed the controllers to obtain the synchronization between the chaotic systems. To establish the efficacy of the methods computations have been carried out. Excellent agreement between the analytical and computational studies has been observed. The achieved synchronization is illustrated in field of secure communication. The results have been compared with published literature.

A color image privacy scheme established on nonlinear system of coupled differential equations

In this manuscript, an encryption technique is developed using a coupled chaotic system of differential equations. The lengthy process of recurring rounds of encryption consumes more space and time on the computing systems demands simple but yet applicable scheme of image encryption, which opens the gateway of the utilization of complex and nonlinear chaotic systems. The proposed image encryption procedure is fast as implementation is concerned because of containing only one round, furthermore, it is found resistant against any type of differential and linear attacks due to the large keyspace and involvement of complex mathematical systems. The third order nonlinearity of Rabinovich-Fabrikant (RF) system of differential equations generates rich and complex chaotic dynamics. Initially, this system is used to generate three chaotic sequences of pseudorandom numbers from the numerical solution of RF system. Then, a color image being converted into three layers is passed from three mathematical operations i.e. XOR, permutation and substitution to create confusion and diffusion in them to generate enciphered image. Moreover, encrypted images successfully passed the NIST SP-800 test and encryption analyses like correlation, histogram and information entropy etc.

From Quantum Physics to Quantum Hypnosis: A Quantum Mind Perspective

ABSTRACT A novel, heuristic model based upon chaotic complex systems theory and quantum mechanics is proposed to overcome the dichotomy between mind and body. The mind–body interface represents a chaotic system, ruled by the probability principle, as shown in quantum mechanics. Neuronal activity shows many patterns of chaotic behavior, and applications of chaotic patterns seem to be relevant for research regarding the mind–body relationship and the process of trance. A quantum consciousness theory has been proposed, largely controversial, since quantum physics applies to subatomic world and not to macrostructures, such as the brain. Quantum cognition is an emerging field that applies the formalism of quantum theory to model cognitive phenomena such as information processing by the human brain; it overcomes limits and shortcomings of cartesian dualism as well as quantum general theory. As hypnosis is a state of consciousness, it applies to hypnotic cognitive functioning rather than hypnotic structure.