In this paper, on the basis of three-dimensional Chen system, a smooth continuous nonlinear flux-controlled memristor model is used as positive feedback term hyper-chaotic circuit system successfully constructed, and simulated equivalent built for simulation using Multisim software, which agrees with numerical results by comparison. Meanwhile, new impulsive control mode called three-stage-impul...

In this paper, we prove that there exists globally exponential attractive and positive invariant set for a general chaotic system, which does not belong to the known Lorenz system, or the Chen system, or the Lorenz family. We show that all the solution orbits of the chaotic system are ultimately bounded with exponential convergent rates and the convergent rates are explicitly estimated. The met...

In this paper, we prove that the Chen system with a set of chaotic parameters is not smoothly equivalent to the Lorenz system with any parameters.

This paper investigates the global chaos synchronization of identical Lü-Chen-Cheng four-scroll chaotic systems (Lü, Chen and Cheng, 2004) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Lü-Chen-Cheng four-scroll chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for th...

In this paper, the existence and uniqueness of solution for fractional order Chen chaotic system is investigated theoretically based on the qualitative theory. The stability of the corresponding equilibria is also investigated similar to the integer order counterpart. According to the obtained results, the bifurcation conditions of these two systems are significantly different. Numerical simula...

A novel solution to the fraction chaotic Chen system is presented in this paper by using the step homotopy analysis method. This method yields a continuous solution in terms of a rapidly convergent infinite power series with easily computable terms. Moreover, the residual error of the SHAM solution is defined and computed for each time interval. Via the computing of the residual error we observ...

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on L...

This paper presents the application of three optimization algorithms to increase chaotic behavior fractional order Chen system. is achieved by optimizing maximum Lyapunov exponent (MLE). The applied techniques are evolutionary (EAs), namely: differential evolution (DE), particle swarm (PSO), and invasive weed (IWO). In each algorithm, process performed using 100 individuals generations from 50 ...

In this paper, we create a multi-scroll chaotic attractor from Chen system by a nonlinear feedback control. The dynamic behavior of the new chaotic attractor is analyzed. Specially, the Lyapunov spectrum and Lyapunov dimension are calculated and the bifurcation diagram is sketched. Furthermore, via changing the value of the control parameters, we can increase the number of equilibrium points an...