Application of CSK Encryption Algorithm in Video Synergic Command Systems

Video command and dispatch systems have become essential communication safeguard measures in circumstances of emergency rescue, epidemic prevention, and control command as, data security has become especially important. After meeting the requirements of voice and video dispatch, this paper proposes an end-to-end encryption method of multimedia information that introduces a multiple protection mechanism including selective encryption and selective integrity protection. The method has a network access authentication and service encryption workflow, which implants startup authentication and key distribution into the information control signaling procedure. This method constitutes a key pool with the three-dimensional Lorenz System, the four-dimensional Cellular Neural Network (CNN) System and the four-dimensional Chen System where the key source system and initial conditions are decided by the plaintext video frame itself. Then, this method optimizes the chaotic sequences to further enhance system security.

Two-Dimensional Manifolds of Modified Chen System with Time Delay

Two-dimensional unstable manifolds of the modified Chen system are constructed at equilibrium solution by “expanding up” along the unstable eigen-direction, hence it is tangent to the unstable eigenspace. In general, unstable manifold expands to the attraction basin of the corresponding limit cycle or attractor. With the introduction of time delay, the two-dimensional unstable manifold of an unstable focus is simulated via expanding solution orbits with restriction condition on the associated foliations. The simulated unstable manifold coincides with the attraction basin of the limit cycle of the delay differential equations.

Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms

This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), particle swarm optimization (PSO), and invasive weed optimization (IWO). In each algorithm, the optimization process is performed using 100 individuals and generations from 50 to 500, with a step of 50, which makes a total of ten independent runs. The results show that the optimized fractional order chaotic Chen systems have higher maximum Lyapunov exponents than the non-optimized system, with the DE giving the highest MLE. Additionally, the results indicate that the chaotic behavior of the fractional order Chen system is multifaceted with respect to the parameter and fractional order values. The dynamical behavior and complexity of the optimized systems are verified using properties, such as bifurcation, LE spectrum, equilibrium point, eigenvalue, and sample entropy. Moreover, the optimized systems are compared with a hyper-chaotic Chen system on the basis of their prediction times. The results show that the optimized systems have a shorter prediction time than the hyper-chaotic system. The optimized results are suitable for developing a secure communication system and a random number generator. Finally, the Halstead parameters measure the complexity of the three optimization algorithms that were implemented in MATLAB. The results reveal that the invasive weed optimization has the simplest implementation.

On Generalized Fractional Dynamical System With Order Lying in (0, 2): Stability Analysis, Chaotic Behaviour, Control and Synchronization

The generalized fractional dynamical system with order lying in (0, 2) is investigated. We present the stability analysis of that system using Mittag-Leffler function, the Gronwall-Bellman Lemma and Laplace transform. The bifurcation diagram of generalized fractional-order Chen system is given. We investigate a theorem to control the chaotic generalized fractional-order systems by linear feedback control. Two examples to achieve the theorem of control are given. The synchronization between two different chaotic generalized fractional systems is presented. We give a theorem to calculate the control functions which achieve synchronization. This theorem is applied to achieve the synchronization between different generalized fractional-order systems with order lying in (0, 1]. And, also, used to achieve the synchronization between the identical generalized fractional-order L\"{u} systems with order lying in [1, 2). There exist an agreement among analytical results and numerical treatments for stability, control and synchronization theorems.

Boundedness of the complex Chen system

<p style='text-indent:20px;'>Some ultimate bounds are derived for the complex Chen system.</p>

Chaos Detection of the Chen System with Caputo–Hadamard Fractional Derivative

In this paper, we investigate the chaotic behaviors of the Chen system with Caputo–Hadamard derivative. First, we construct some practical numerical schemes for the Chen system with Caputo–Hadamard derivative. Then, by means of the variational equation, we estimate the bounds of the Lyapunov exponents for the considered system. Furthermore, we analyze the dynamical evolution of the Chen system with Caputo–Hadamard derivative based on the Lyapunov exponents, and we found that chaos does exist in the considered system. Some phase diagrams and Lyapunov exponent spectra are displayed to verify our analysis.

A New 4D Four-Wing Memristive Hyperchaotic System: Dynamical Analysis, Electronic Circuit Design, Shape Synchronization and Secure Communication

In this paper, a simple four-wing chaotic attractor is first proposed by replacing the constant parameters of the Chen system with a periodic piecewise function. Then, a new 4D four-wing memristive hyperchaotic system is presented by adding a flux-controlled memristor with linear memductance into the proposed four-wing Chen system. The memristor mathematical structure model is simple and easy to implement. Dynamical analysis and numerical simulation of the memristive hyperchaotic system are carried out. Then, the electronic circuit of the hyperchaotic system is designed and implemented. The results of numerical simulation are in good agreement with the electronic circuit experiment. In addition, shape synchronization control for the 4D four-wing memristive hyperchaotic system is realized, and a communication system is designed by using the shape synchronization method. Finally, secure signal masking application is implemented on Matlab platform. In the developed secure communication scheme, the information signal overlaps with the chaotic masking signal, which improves the security of the system.