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.

Time-Delay Characteristics of Complex Lü System and Its Application in Speech Communication

Although complex Lü systems have been considered in many studies, application of the self-time-delay synchronization (STDS) of complex Lü systems in secure speech communications does not appear to have been covered in much of the literature. Therefore, it is meaningful to study the STDS of complex Lü systems and its application in secure speech communication. First, a complex Lü system with double time-delay is introduced and its chaotic characteristics are analyzed. Second, a synchronization controller is designed to achieve STDS. Third, the improved STDS controller is used to design a speech communication scheme based on a complex Lü system. Finally, the effectiveness of the controller and communication scheme are verified by simulation.

Secured Color Image Compression based on Compressive Sampling and Lü System

An efficacious and unharmed approach is vital for transmission of sensitive and secret images over unsecure public Internet. In this paper, secured color image compression method based on compressive sampling and Lü system is proposed. Initially, the plain-image is sparsely represented in transform basis. Compressive sampling measurements are obtained from these sparse transform coefficients by employing incoherent sensing matrix. To upgrade the security level, permutation-substitution operations are performed on pixels based on Lü system. To concoct input sensitivity in the scheme, the keys are obtained from input image. Lastly, fast and efficient greedy algorithm is utilized for sparse signal reconstruction. To evaluate the performance of the proposed scheme Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM), Average Difference (AD), Structural Content (SC), Normalized Cross Correlation (NCC), Normalized Absolute Error (NAE), Edge Strength Similarity (ESSIM), Maximum Difference (MD), Correlation Coefficient, Unified Average Changing Intensity (UACI), Key Sensitivity, Number of pixel change Rate (NPCR), Key Space and Histogram metrics are used. Experimental results demonstrate that the proposed scheme produced highly satisfactory security.

Multistability and Formation of Spiral Waves in a Fractional-Order Memristor-Based Hyperchaotic Lü System with No Equilibrium Points

Multistablity analysis and formation of spiral wave in the fractional-order nonlinear systems is a recent hot topic. In this paper, dynamics, coexisting attractors, complexity, and synchronization of the fractional-order memristor-based hyperchaotic Lü system are investigated numerically by means of bifurcation diagram, Lyapunov exponents (LEs), chaos diagram, and sample entropy (SampEn) algorithm. The results show that the system has rich dynamics and high complexity. Meanwhile, coexisting attractors in the system are observed and hidden dynamics are illustrated by changing the initial conditions. Finally, the network based on the system is built, and the emergence of spiral waves is investigated and chimera states are observed.

An efficient novel color image encryption algorithm based on 3D Lü chaotic dynamical system and SHA-512

In this paper, an efficient novel dual permutation–substitution structure-based color image encryption algorithm is proposed. Initially, the Secure Hash Algorithm-512 (SHA-512) is applied to the input image to generate the initial values for the Lü system dynamically. In the first stage of permutation, inter-color-component pixel shuffling is carried out with a circular pixel-swapping mechanism. In the second stage, intra-color-component pixel shuffling is executed, based on pseudorandom positions generated by the Lü chaotic system. Pixel values are changed in the substitution stage, based on float-valued chaotic sequences generated by the Lü system. The performance of the proposed algorithm is evaluated with metrics such as key space, key sensitivity, histograms, correlation coefficients (vertical, horizontal and diagonal), information entropy, number of pixel changes rate (NPCR), unified average changing intensity (UACI), peak signal-to-noise ratio (PSNR), mean absolute error (MAE), contrast analysis, encryption time and the National Institute of Standards and Technology Special Publication 800-22 (NIST SP 800-22) statistical test. The experimental results obtained and performance assessment show that the proposed scheme has produced good results.

Coexisting Attractors, Energy Analysis and Boundary of Lü System

In this study, first, the phenomenon of multistability in the Lü system is found, which shows the coexistence of two different point attractors and one chaotic attractor. These coexisting attractors are dependent on initial conditions of the system while the parameters of the system are fixed. Then, the Lü system is transformed to a Kolmogorov-type system, which includes the conservative torque consisting of the inertial torque and the internal torque, the dissipative torque, and the external torque. Moreover, by analyzing the combination of different types of torques and investigating the cycling of energy based on the Casimir function and Hamiltonian function, the interaction between the external torque and other torques is found to be the main reason for the Lü system to generate chaos. Finally, by investigating the Casimir function, it is found that the boundary of the Lü system is only related to system parameters.