Dynamical analysis and anti-synchronization of a new 6D model with self-excited attractors

A novel 6D dissipative model with an unstable equilibrium point is introduced herein.Some of the dynamic characteristics of the proposed model were explored via analyses and numerical simulations including critical points,stability,Lyapunov exponents,time phase portraits,and circuit implementation.Also,anti-synchronization phenomena were implemented on the new system.Firstly,the error dynamics is found.Then,four different controllers are adopted to stabilize this error relying on the nonlinear control technique with two main ways:linearization and Lyapunov stability theory.In comparison with previous works,the present controllers realize anti-synchronization based on another method/linearization method.Finally,a comparison between the two ways was made.The simulation results show the effectiveness and accuracy of the first analytical strategy.

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional （3D） continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation.

Anti-synchronization in Different Hyperchaotic Systems

Based on active control theory, anti-synchronization between two different hyperchaotic systems is investigated. The sufficient conditions for achieving anti-synchronization of two different hyperchaotic systems are derived. Moreover, numerical simulations are presented for hyperehaotic Lorenz-Chen system, hyperchaotic Lorenz-Lu system, and hyperchaotic Chen Lu system to verify the effectiveness and feasibility of the proposed anti-synchronization scheme.

Anti-synchronization Between Lorenz and Liu Hyperchaotic Systems

Anti-synchronization between different hyperchaotic systems is presented using Lorenz and Liu systems. When the parameters of two systems are known, one can use active synchronization. When the parameters are unknown or uncertain, the adaptive synchronization is applied. The simulation results verify the effectiveness of the proposed two schemes for anti-synchronization between different hyperchaotic systems.

Anti-synchronization of a new hyperchaotic system via small-gain theorem

Based on the small-gain theorem, the anti-synchronization between two identical new hyperchaotic systems is investigated, moreover, the general sufficient conditions to achieve anti-synchronization between the new hyperchaotic system and the new hyperchaotic Lorenz system are obtained via small-gain theorem. Numerical simulations are performed to verify and illustrate the analytical results.

Anti-synchronization Between Coupled Networks with Two Active Forms

This paper studies anti-synchronization and its control between two coupled networks with nonlinear signal＇s connection and the inter-network actions. If anti-synchronization does not exist between two such networks, adaptive controllers are designed to anti-synchronize them. Different node dynamics and nonidentical topological structures are considered and useful criteria for anti-synchronization between two networks are given. Numerical examples are presented to show the efficiency of our derived results.

Memristor-based hyper-chaotic circuit for image encryption

The memristor is a kind of non-linear element with memory function,which can be applied to chaotic systems to increase signal randomness and complexity.In this paper,a new four-dimensional hyper-chaotic system is designed based on a flux controlled memristor model,which can generate complex chaotic attractors.The basic dynamic theory analysis and numerical simulations of the system,such as the stability of equilibrium points,the Lyapunov exponents and dimension,Poincare maps,the power spectrum,and the waveform graph prove that it has rich dynamic behaviors.Then,the circuit implementation of this system is established.The consistency of simulation program with integrated circuit emphasis(SPICE)simulation and numerical analysis proves the ability to generate chaos.Finally,a new image encryption scheme is designed by using the memristor-based hyper-chaotic system proposed in this paper.The scheme involves a total of two encryptions.By using different security analysis factors,the proposed algorithm is compared with other image encryption schemes,including correlation analysis,information entropy,etc.The results show that the proposed image encryption scheme has a large key space and presents a better encryption effect.

A simple method to simultaneously achieve synchronization and anti-synchronization in chaotic systems

In this paper, a novel adaptive control approach is presented to simultaneously achieve synchronization and antisynchronization in partially linear chaotic systems. Through appropriately separating state vectors of such systems, synchronization and anti-synchronization could be simultaneously realized in different subspaces, which may be strictly proven theoretically. Simulation results for a Lorenz chaotic system and a new hyper-chaotic system are provided to illustrate the effectiveness of the proposed method. Finally, a new secure communication scheme based on such a synchronization phenomenon of the hyper-chaotic system is demonstrated. Numerical results show success in transmitting a periodic signal with high security.

Applications of modularized circuit designs in a new hyper-chaotic system circuit implementation

Modularized circuit designs for chaotic systems are introduced in this paper.Especially,a typical improved modularized design strategy is proposed and applied to a new hyper-chaotic system circuit implementation.In this paper,the detailed design procedures are described.Multisim simulations and physical experiments are conducted,and the simulation results are compared with Matlab simulation results for different system parameter pairs.These results are consistent with each other and they verify the existence of the hyper-chaotic attractor for this new hyper-chaotic system.

Hybrid Synchronization of a Chen Hyper-Chaotic System with Two Simple Linear Feedback Controllers

This paper brings attention on the hybrid synchronization of the Chen hyper-chaotic system by using some simple controllers. We give the sufficient conditions for achieving the goal by using the Lyapunov stability theory, and we verify our conclusion by numerical simulations.

Adaptive Anti-Synchronization Between Different Chaotic/Hyperchaotic Systems with Fully Unknown Parameters

The anti-synchronization between different chaotic/hyperchaotic systems with fully unknown parameters is considered in detail. Based on Lyapunov stability theory, the adaptive control schemes and parameter update rules are designed in this paper. Two numerical examples show the effectiveness and feasibility of the proposed method.

ANTI-SYNCHRONIZATION OF TWO TIME-DELAY BIDIRECTIONAL COUPLING HYPERCHAOTIC SYSTEMS VIA NONLINEAR CONTROL

In this paper we study the chaos synchronization and anti-synchronization problems between two hyper-chaotic systems with bidirectional coupling,and present synchronization and anti-synchronization methods of chaotic systems,based on timedelayed feedback.Coupling coefficients between the drive and response systems are different,which are supposed to be nonlinearly coupled.Based on the nonlinear control theory,the synchronization and anti-synchronization between two different time-delay hyper-chaotic systems are investigated.The condition of synchronization is derived according to the error dynamical systems.Numerical simulations show the effectiveness and feasibility of the proposed synchronous conditions.

An Image Encryption Approach Using a Shuffling Map

A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyvalues of the shuffled image according to the changed chaotic values of the same position between the above nonlinearchaotic sequence and the sorted chaotic sequence.The experimental results demonstrate that the image encryptionscheme based on a shuffling map shows advantages of large key space and high-level security.Compared with someencryption algorithms,the suggested encryption scheme is more secure.

Anti-synchronization Between Two Coupled Networks with Unknown Parameters Using Adaptive and Pinning Controls

In this paper, we study anti-synchronization between two coupled networks where the node dynamics has an unknown system parameter. By designing adaptive and pinning control schemes, we realize the anti-synchronization.By Lyapunov stability theory, we obtain two theorems on the appearance of anti-synchronization. In addition, we derive a criterion for the pinning number of nodes. Finally we provide two numerical examples to show the effectiveness of our proposed control schemes. When the anti-synchronization is achieved, we successfully identify the unknown system parameter.

Synchronization Phenomena Investigation of a New Nonlinear Dynamical System 4D by Gardano’s and Lyapunov’s Methods

Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The findings have allowed authors to develop two analytical approaches using the second Lyapunov(Lyp)method and the Gardanomethod.Since the Gardano method does not involve the development of special positive Lyp functions,it is very efficient and convenient to achieve excessive systemSYCR phenomena.Error is overcome by using Gardano and overcoming some problems in Lyp.Thus we get a great investigation into the convergence of error dynamics,the authors in this paper are interested in giving numerical simulations of the proposed model to clarify the results and check them,an important aspect that will be studied is Synchronization Complete hybrid SYCR and anti-Synchronization,by making use of the Lyapunov expansion analysis,a proposed control method is developed to determine the actual.The basic idea in the proposed way is to receive the evolution of between two methods.Finally,the present model has been applied and showing in a new attractor,and the obtained results are compared with other approximate results,and the nearly good coincidence was obtained.

Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication

This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.

Color-image encryption scheme based on channel fusion and spherical diffraction

A secure encryption scheme for color images based on channel fusion and spherical diffraction is proposed in this paper. In the proposed encryption scheme, a channel fusion technology based on the discrete wavelet transformation is used to transform color images into single-channel grayscale images, firstly. In the process of transformation, the hyperchaotic system is used to permutate and diffuse the information of red–green–blue(RGB) channels to reduce the correlation of channels. Then the fused image is encrypted by spherical diffraction transform. Finally, the complex-valued diffraction result is decomposed into two real parts by the improved equal module decomposition, which are the ciphertext and the private key. Compared with the traditional color image encryption schemes that encrypt RGB channels separately, the proposed scheme is highly secure and robust.

Generation of Hyperchaos from the LüSystem with a Sinusoidal Perturbation

This paper introduces a hyperchaotic system from the Lü system with a sinusoïdal perturbation. This hyperchaotic system has more complex dynamical behaviors, and can generate 2-scroll hyperchaotic attractor and 2-scroll chaotic attractor under different control parameters. Theoretical analyses and simulation are conducted to investigate the dynamical behaviors of the proposed hyperchaotic system by means of Lyapunov exponents, analysis of the bifurcation diagram and phase portraits.

Anti-synchronization of Chaotic Neural Networks with Time Delay

In the paper, the anti-synchronization problem of the general delayed chaotic neural networks is investigated. For the master and slave systems, we obtain a control law to achieve the state anti-synchronization of two identical chaotic neural networks. By using the Halanay inequality lemma and Lyapunov stability method, we derive a delay indepen- dent sufficient exponential anti-synchronization condition relative to the parameters of the systems and controller gain matrix. The condition is easily verified in practice. Finally, the theoretical results are applied to two delayed chaotic neural networks, and numerical simulations are given to demonstrate the performance of the proposed scheme throughout some examples.