has been much studied for positive values of its parameters (a, b, c) and has chaotic solutions for typical parameters of (35, 3, 28). Recently, Algaba et al. [2013] have shown that the Chen system has only two independent parameters a/c and b/c and that it is identical to the reversed-time Lorenz system for c > 0 and to the forward-time Lorenz system for c < 0 in the parameter plane ρ + σ = −1...

A new controller design method is proposed to synchronize the fractional-order hyperchaotic system through the stability theory of fractional calculus; the synchronization between two identical fractional-order Chen hyperchaotic systems is realized by designing only two suitable controllers in the response system. Furthermore, this control scheme can be used in secure communication via the tech...

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncerta...

Adaptive controllers are designed to synchronize two different chaotic systems with uncertainties, including unknown parameters, internal and external perturbations. Lyapunov stability theory is applied to prove that under some conditions the drive-response systems can achieve synchronization with uniform ultimate bound even though the bounds of uncertainties are not known exactly in advance. T...

In the information security field, the substitution boxes (S-boxes) have been extensively used in many cryptographic systems. This paper presents a novel approach for generating dynamically cryptographically S-boxes using a four-dimensional hyperchaotic Lorenz system. Within the algorithm, the initial condition is employed to drive the hyper-chaotic system to generate a chaotic sequence which i...

In this paper, the multi-state synchronization of chaotic systems with non-identical, unknown, and time-varying delay in presence external perturbations parametric uncertainties was studied. The unknown delays, bounds disturbance uncertainty, as well changes system parameters complicate determination control function synchronization. During a scheme using robust-adaptive procedure help Lyapunov...

Since the idea of synchronizing chaotic systems was introduced by Pecora and Carroll[1] in 1990, chaos synchronization has received increasing attention due to its theoretical challenge and its great potential applications in secure communication,chemical reaction and biological systems[2]. Recently several different types of synchronizations have been proposed in the literature, for example, g...

In this paper, the periodic, quasi periodic and chaotic responses of rotational machines with a hexagonal centrifugal governor are studied. The external disturbance is assumed as a sinusoid effect. By using the forth order Rung-Kutta numerical integration method, bifurcation diagram, largest Lyapunov exponent and Lyapunov dimension are calculated and presented to detect the critical controlling...

ToToday’s market place is increasingly dynamic and volatile. In this area supply network issues recently have attracted a lot of attention from industrial practitioners and academics worldwide. Chaos theory is the study of complex, nonlinear, dynamic systems. For chaotic systems, a tiny change in conditions may result in an enormous change in system output, whereas substantial changes in condit...

Chaotic simulated annealing (CSA) proposed by Chen and Aihara has been successfully used to solve a variety of combinatorial optimization problems. CSA uses a penalty term to enforce solution validity as in the original Hopfield-Tank approach. There exists a conflict between solution quality and solution validity in the penalty approach. It is often difficult to adjust the relative magnitude of...