Local Dynamics Analysis of a Four-Dimensional Hyperchaotic Lorenz System

The local dynamical behaviors of a four-dimensional hyperchaotic Lorenz system, including stability and bifurcations, are investigated in this paper by analytical and numerical methods. The equilibriums and their stability under different parameter conditions are analyzed by applying Routh-Hurwitz criterion. The results indicate that the system may exist one, three and five equilibrium points for different system parameters. Based on the central manifold theorem and normal form theorem, the pitchfork bifurcation and Hopf bifurcation are studied respectively. By using the Hopf bifurcation theorem and calculating the first Lyapunov coefficient, the Hopf bifurcation of this system is obtained as supercritical for certain parameters. Finally, the results of theoretical parts are verified by some numerical simulations.

A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system

We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.

A new four-dimensional hyperchaotic Lorenz system and its adaptive control

Based on the Lorenz chaotic system, this paper constructs a new four-dimensional hyperchaotic Lorenz system, and studies the basic dynamic behaviours of the system. The Routh-Hurwitz theorem is applied to derive the stability conditions of the proposed system. Furthermore, based on Lyapunov stability theory, an adaptive controller is designed and the new four-dimensional hyperchaotic Lorenz system is controlled at equilibrium point. Numerical simulation results are presented to illustrate the effectiveness of this method.

Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system

This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.

Identification and Control of Hyperchaotic Lorenz System Based on Quantum Inspired PSO and Wavelet Neural Network

For the identification and control problem of hyperchaotic Lorenz system,a method of feedback compensation control based on quantum inspired PSO and wavelet neural network(PSOQI-Wavelet Neural Network)is proposed.Firstly,the quantum principle obtained from Quantum PSO(QPSO)has been combined with standard PSO to form a new hybrid algorithm called PSO with Quantum Infusion(PSO-QI).Then,the parameters of wavelet neural network were optimized with PSO-QI and feedback compensation control for hyperchaotic Lorenz system is implemented using optimized PSOQI-Wavelet Neural Network.The numerical simulation results showed that this method has better precision and can quickly track given hyperchaotic Lorenz system.

Medical Image Encryption Based on Josephus Traversing and Hyperchaotic Lorenz System

This study proposes a new medical image encryption scheme based on Josephus traversing and hyper-chaotic Lorenz system.First,a chaotic sequence is generated through hyperchaotic system.This hyperchaotic sequence is used in the scrambling and diffusion stages of the algorithm.Second,in the scrambling process,the image is initially confused by Josephus scrambling,and then the image is further confused by Arnold map.Finally,generated hyperchaos sequence and exclusive OR operation is used for the image to carry on the positive and reverse diffusion to change the pixel value of the image and further hide the effective information of the image.In addition,the information of the plaintext image is used to generate keys used in the algorithm,which increases the ability of resisting plaintext attack.Experimental results and security analysis show that the scheme can effectively hide plaintext image information according to the characteristics of medical images,and is resistant to common types of attacks.In addition,this scheme performs well in the experiments of robustness,which shows that the scheme can solve the problem of image damage in telemedicine.It has a positive significance for the future research.

Synchronization of hyperchaotic Lorenz system based on passive control

Synchronization of a hyperchaotic Lorenz system is discussed using passive control. Based on the properties of a passive system, a passive controller is designed and the synchronization between two hyperchaotic Lorenz systems under different initial conditions is realized. Simulation results show the proposed synchronization method to be effective.