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Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Djennoune Said, Bettayeb Maamar, Al-Saggaf Ubaid Muhsen

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 1

179--194

This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.

Chaos synchronization of uncertain coronary artery systems through sliding mode

Qian D. W., Xi Y. F., Tong S. W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 3

455--462

The chaotic phenomena of coronary artery systems are hazardous to health and may induce illness development. From the perspective of engineering, the potential harm can be eliminated by synchronizing chaotic coronary artery systems with a normal one. This paper investigates the chaos synchronization problem in light of the methodology of sliding mode control (SMC). Firstly, the nonlinear dynamics of coronary artery systems are presented. Since the coronary artery systems suffer from uncertainties, the technique of derivative-integral terminal SMC is employed to achieve the chaos synchronization task. The stability of such a control system is proven in the sense of Lyapunov. To verify the feasibility and effectiveness of the proposed method, some simulation results are illustrated in comparison with a benchmark.

Synchronization of an uncertain Duffing oscillator with higher order chaotic systems

Kabziński J.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 4

625--634

The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing–Arneodo and Duffing–Chua synchronization problems.