This paper is concerned with chaotification of discrete dynamical systems in Banach spaces via feedback control techniques. A criterion of chaos in Banach spaces is first established. This criterion extends and improves the Marotto theorem. Discussions are carried out in general and some special Banach spaces. All the controlled systems are proved to be chaotic in the sense of both Devaney and ...

This paper discusses the design of active controllers for generalized projective synchronization (GPS) of identical Li 2-scroll chaotic systems (Li, 2009), identical Lü-Chen 2-scroll chaotic systems (Lü and Chen, 2002) and non-identical Li and Lü-Chen 2-scroll systems. The synchronization results (GPS) derived in this paper for the 2-scroll chaotic systems have been derived using active control...

In this article, the active control method is used for hybrid synchronization between two fractional order hyperchaotic systems, Chen hyperchaotic system taken as the master system and the other fractional order hyperchaoticLu system taken as slave system separately. The fractional derivative is described in Caputo sense. Numerical simulation results which are carried out using Adams–Bashforth–...

This paper centres on the application of the new piecewise successive linearization method PSLM in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including thos...

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper a chaotic communication method using extended Kalman filter is presented. The chaotic synchronization is implemented by EKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication is used to achieve a satisfactory, typical se...

In this article, we investigate the synchronization of uncertain chaotic systems. Based upon the parameters identification technique and a simple but efficient control method, we control the response system to be the drive system with parameters unknown. The techniques are successfully applied to Lorenz system and Chen system. Furthermore, the effect of external noise is under our discussion. 2...

This paper proposes a novel image block encryption algorithm based on three-dimensional Chen chaotic dynamical system. The algorithm works on 32-bit image blocks with a 192-bit secret key. The idea is that the key is employed to drive the Chen’s system to generate a chaotic sequence that is inputted to a specially designed function G, in which we use new 8x8 S-boxes generated by chaotic maps (T...

Abstract: This paper shows that a large class of chaotic systems, introduced in (Čelikovský and Vaněček, 1994), (Vaněček and Čelikovský, 1996) as the generalized Lorenz system, can be further generalized to the hyperbolic-type generalized Lorenz system. While the generalized Lorenz system unifies both the famous Lorenz system and new Chen’s system (Ueta and Chen, 1999), (Chen and Ueta, 2000), t...

In this paper we present a new version of Chen’s system — a piecewise linear Chen system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also mulistability, i.e. the existence of small parameter windows where, for some fixed bifurcation parameter and depending on initial...