Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities.

Chaotic CS Encryption:An Efficient Image Encryption Algorithm Based on Chebyshev Chaotic System and Compressive Sensing

Images are the most important carrier of human information. Moreover, how to safely transmit digital imagesthrough public channels has become an urgent problem. In this paper, we propose a novel image encryptionalgorithm, called chaotic compressive sensing (CS) encryption (CCSE), which can not only improve the efficiencyof image transmission but also introduce the high security of the chaotic system. Specifically, the proposed CCSEcan fully leverage the advantages of the Chebyshev chaotic system and CS, enabling it to withstand various attacks,such as differential attacks, and exhibit robustness. First, we use a sparse trans-form to sparse the plaintext imageand then use theArnold transformto perturb the image pixels. After that,we elaborate aChebyshev Toeplitz chaoticsensing matrix for CCSE. By using this Toeplitz matrix, the perturbed image is compressed and sampled to reducethe transmission bandwidth and the amount of data. Finally, a bilateral diffusion operator and a chaotic encryptionoperator are used to perturb and expand the image pixels to change the pixel position and value of the compressedimage, and ultimately obtain an encrypted image. Experimental results show that our method can be resistant tovarious attacks, such as the statistical attack and noise attack, and can outperform its current competitors.

Rucklidge-based memristive chaotic system:Dynamic analysis and image encryption

A new four-dimensional(4D)memristive chaotic system is obtained by introducing a memristor into the Rucklidge chaotic system,and a detailed dynamic analysis of the system is performed.The sensitivity of the system to parameters allows it obtains 16 different attractors by changing only one parameter.The various transient behaviors and excellent spectral entropy and C0 complexity values of the system can also reflect the high complexity of the system.A circuit is designed and verified the feasibility of the system from the physical level.Finally,the system is applied to image encryption,and the security of the encryption system is analyzed from multiple aspects,providing a reference for the application of such memristive chaotic systems.

Data encryption based on a 9D complex chaotic system with quaternion for smart grid

With the development of smart grid, operation and control of a power system can be realized through the power communication network, especially the power production and enterprise management business involve a large amount of sensitive information, and the requirements for data security and real-time transmission are gradually improved. In this paper, a new 9-dimensional(9D) complex chaotic system with quaternion is proposed for the encryption of smart grid data. Firstly, we present the mathematical model of the system, and analyze its attractors, bifurcation diagram, complexity,and 0–1 test. Secondly, the pseudo-random sequences are generated by the new chaotic system to encrypt power data.Finally, the proposed encryption algorithm is verified with power data and images in the smart grid, which can ensure the encryption security and real time. The verification results show that the proposed encryption scheme is technically feasible and available for power data and image encryption in smart grid.

Bipolar-growth multi-wing attractors and diverse coexisting attractors in a new memristive chaotic system

This article proposes a non-ideal flux-controlled memristor with a bisymmetric sawtooth piecewise function, and a new multi-wing memristive chaotic system(MMCS) based on the memristor is generated. Compared with other existing MMCSs, the most eye-catching point of the proposed MMCS is that the amplitude of the wing will enlarge towards the poles as the number of wings increases. Diverse coexisting attractors are numerically found in the MMCS, including chaos,quasi-period, and stable point. The circuits of the proposed memristor and MMCS are designed and the obtained results demonstrate their validity and reliability.

A Speech Cryptosystem Using the New Chaotic System with a Capsule-Shaped Equilibrium Curve

In recent years,there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle,butterfly,heart and apple.This paper describes a new 3-D chaotic dynamical system with a capsule-shaped equilibrium curve.The proposed chaotic system has two quadratic,two cubic and two quartic nonlinear terms.It is noted that the proposed chaotic system has a hidden attractor since it has an infinite number of equilibrium points.It is also established that the proposed chaotic system exhibits multi-stability with two coexisting chaotic attractors for the same parameter values but differential initial states.A detailed bifurcation analysis with respect to variations in the system parameters is portrayed for the new chaotic system with capsule equilibrium curve.We have shown MATLAB plots to illustrate the capsule equilibrium curve,phase orbits of the new chaotic system,bifurcation diagrams and multi-stability.As an engineering application,we have proposed a speech cryptosystem with a numerical algorithm,which is based on our novel 3-D chaotic system with a capsule-shaped equilibrium curve.The proposed speech cryptosystem follows its security evolution and implementation on Field Programmable Gate Array(FPGA)platform.Experimental results show that the proposed encryption system utilizes 33%of the FPGA,while the maximum clock frequency is 178.28 MHz.

Video Transmission Secrecy Improvement Based on Fractional Order Hyper Chaotic System

In the Digital World scenario,the confidentiality of information in video transmission plays an important role.Chaotic systems have been shown to be effective for video signal encryption.To improve video transmission secrecy,compressive encryption method is proposed to accomplish compression and encryption based on fractional order hyper chaotic system that incorporates Compressive Sensing(CS),pixel level,bit level scrambling and nucleotide Sequences operations.The measurement matrix generates by the fractional order hyper chaotic system strengthens the efficiency of the encryption process.To avoid plain text attack,the CS measurement is scrambled to its pixel level,bit level scrambling decreases the similarity between the adjacent measurements and the nucleotide sequence operations are done on the scrambled bits,increasing the encryption.Two stages are comprised in the reconstruction technique,the first stage uses the intra-frame similarity and offers robust preliminary retrieval for each frame,and the second stage iteratively improves the efficiency of reconstruction by integrating inter frame Multi Hypothesis(MH)estimation and weighted residual sparsity modeling.In each iteration,the residual coefficient weights are modified using a mathematical approach based on the MH predictions,and the Split Bregman iteration algorithm is defined to resolve weighted l1 regularization.Experimental findings show that the proposed algorithm provides good compression of video coupled with an efficient encryption method that is resistant to multiple attacks.

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with Caputo Fractional Derivative

Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this paper introduces a high-precision numerical approach.Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method.We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies.We investigate the influence of α_(1),α_(2),α_(3) on the numerical solution of fractional-order Lorenz chaotic systems.The simulation results of integer order are in good agreement with those of othermethods.The simulation results of numerical experiments demonstrate the effectiveness of the present method.

Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay

It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system’s parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony(ABC) algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method.

Generating one-,two-,three-and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper,which can exhibit periodic orbit and chaos under the conditions on the system parameters.Importantly,the system can generate one-,two-,three-and four-scroll chaotic attractors with appropriate choices of parameters.Interestingly,all the attractors are generated only by changing a single parameter.The dynamic analysis approach in the paper involves time series,phase portraits,Poincar'e maps,a bifurcation diagram,and Lyapunov exponents,to investigate some basic dynamical behaviours of the proposed four-dimensional system.

The Switching Fractional Order Chaotic System and Its Application to Image Encryption

Many studies on fractional order chaotic systems and secure communications have been carried out, however,switching fractional order chaotic system and its application to image encryption have not been explored yet. In this paper,a new switching fractional order chaotic system is proposed,containing fractional order Chen system and the other two fractional order chaotic systems. Chaotic attractors and dynamical analysis including Lyapunov exponent, bifurcation diagram,fractal dimension, dissipation, stability and symmetry are shown firstly. After that, some circuit simulations through Multisim are presented. By controlling switch k_1 and k_2, switching among the three fractional order chaotic subsystems can be realized. Finally,we apply the switching fractional order chaotic system to image encryption using exclusive or(XOR) encryption algorithm. The encryption scheme could increase randomness and improve speed of encryption.

A novel study on the impulsive synchronization of fractional-order chaotic systems

The stability of impulsive fractional-order systems is discussed.A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems.The synchronization criterion is suitable for the case of the order 0 < q ≤ 1.It is more general than those of the known results.Simulation results are given to show the effectiveness of the proposed synchronization criterion.

Two Types of Adaptive Generalized Synchronization of Chaotic Systems

This paper is concerned with the existence of adaptive generalized synchronization(GS) of two chaotic systems.An adaptive control is designed based on a Lyapunov approach.By using modified system approach,some sufficient conditions for the existence of first two types of adaptive GS inertial manifolds are established.Finally,some numerical simulations are provided to illustrate the theoretical results.

Observer based projective reduced-order synchronization of different chaotic systems

The projective reduced-order synchronization of two different chaotic systems with different orders is investigated based on the observer design in this paper.According to the observer theory,the reduced-order observer is designed.The projective synchronization can be realized by choosing the transition matrix of the observer as a diagonal matrix.Further,the synchronization between hyperchaotic Chen system(fourth order)and Rssler system(third order)is taken as the example to demonstrate the effectiveness of the proposed observer.Numerical simulations confirm the effectiveness of the method.

Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances

We develop an optimal tracking control method for chaotic system with unknown dynamics and disturbances. The method allows the optimal cost function and the corresponding tracking control to update synchronously. According to the tracking error and the reference dynamics, the augmented system is constructed. Then the optimal tracking control problem is defined. The policy iteration(PI) is introduced to solve the min-max optimization problem. The off-policy adaptive dynamic programming(ADP) algorithm is then proposed to find the solution of the tracking Hamilton–Jacobi–Isaacs(HJI) equation online only using measured data and without any knowledge about the system dynamics. Critic neural network(CNN), action neural network(ANN), and disturbance neural network(DNN) are used to approximate the cost function, control, and disturbance. The weights of these networks compose the augmented weight matrix, and the uniformly ultimately bounded(UUB) of which is proven. The convergence of the tracking error system is also proven. Two examples are given to show the effectiveness of the proposed synchronous solution method for the chaotic system tracking problem.

Convergent robust stabilization conditions for fuzzy chaotic systems based on the edgewise subdivision approach

This paper concerns the problem of stabilizing fuzzy chaotic systems via the viewpoint of the edgewise subdivision approach.Firstly,a new edgewise subdivision algorithm is proposed to implement the simplex edgewise subdivision which divides the overall fuzzy chaotic systems into a lot of sub-systems by a kind of algebraic description.These sub-systems have the same volume and shape characteristics.Secondly,a novel kind of control scheme which switches by the transfer of different operating sub-systems is proposed to achieve convergent stabilization conditions for the underlying controlled fuzzy chaotic systems.Finally,a numerical example is given to demonstrate the validity of the proposed methods.

Dynamical analysis,circuit realization,and application in pseudorandom number generators of a fractional-order laser chaotic system

A new five-dimensional fractional-order laser chaotic system(FOLCS)is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system.Dynamical behavior of the system,circuit realization and application in pseudorandom number generators are studied.Many types of multi-stable states are discovered in the system.Interestingly,there are two types of state transition phenomena in the system,one is the chaotic state degenerates to a periodical state,and the other is the intermittent chaotic oscillation.In addition,the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm.Moreover,a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit.Finally,a pseudo-random sequence generator is designed using the FOLCS,and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22.This study enriches the research on the dynamics and applications of FOLCS.

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

A five-value memristor model is proposed,it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current.Then,based on the classical Liu-Chen system,a new memristor-based fourdimensional(4D)chaotic system is designed by using the five-value memristor.The trajectory phase diagram,Poincare mapping,bifurcation diagram,and Lyapunov exponent spectrum are drawn by numerical simulation.It is found that,in addition to the general chaos characteristics,the system has some special phenomena,such as hidden homogenous multistabilities,hidden heterogeneous multistabilities,and hidden super-multistabilities.Finally,according to the dimensionless equation of the system,the circuit model of the system is built and simulated.The results are consistent with the numerical simulation results,which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.

Acoustic wireless communication based on parameter modulation and complex Lorenz chaotic systems with complex parameters and parametric attractors

As the competition for marine resources is increasingly fierce,the security of underwater acoustic communication has attracted a great deal of attention.The information and location of the communicating platform can be leaked during the traditional underwater acoustic communication technology.According to the unique advantages of chaos communication,we put forward a novel communication scheme using complex parameter modulation and the complex Lorenz system.Firstly,we design a feedback controller and parameter update laws in a complex-variable form with rigorous mathematical proofs(while many previous references on the real-variable form were only special cases in which the imaginary part was zero),which can be realized in practical engineering;then we design a new communication scheme employing parameter modulation.The main parameter spaces of the complex Lorenz system are discussed,then they are adopted in our communication scheme.We also find that there exist parametric attractors in the complex Lorenz system.We make numerical simulations in two channels for digital signals and the simulations verify our conclusions.

Solutions and memory effect of fractional-order chaotic system:A review

Fractional calculus is a 300 years topic,which has been introduced to real physics systems modeling and engineering applications.In the last few decades,fractional-order nonlinear chaotic systems have been widely investigated.Firstly,the most used methods to solve fractional-order chaotic systems are reviewed.Characteristics and memory effect in those method are summarized.Then we discuss the memory effect in the fractional-order chaotic systems through the fractionalorder calculus and numerical solution algorithms.It shows that the integer-order derivative has full memory effect,while the fractional-order derivative has nonideal memory effect due to the kernel function.Memory loss and short memory are discussed.Finally,applications of the fractional-order chaotic systems regarding the memory effects are investigated.The work summarized in this manuscript provides reference value for the applied scientists and engineering community of fractional-order nonlinear chaotic systems.