A study on coexistence of different types of synchronization between different dimensional fractional chaotic systems

2017Azar A.T.Book ChapterOuannas A.Radwan A.G.Ziar T.

In this study, robust approaches are proposed to investigate the problem of the coexistence of various types of synchronization between different dimensional fractional chaotic systems. Based on stability theory of linear fractional order systems, the co-existence of full state hybrid function projective synchronization (FSHFPS), inverse generalized synchronization (IGS), inverse full state hybrid projective synchronization (IFSHPS) and generalized synchronization (GS) is demonstrated. Using integer-order Lyapunov stability theory and fractional Lyapunov method, the co-existence of FSHFPS, inverse full state hybrid function projective synchronization (IFSHFPS), IGS and GS is also proved. Finally, numerical results are reported, with the aim to illustrate the capabilities of the novel schemes proposed herein. © Springer International Publishing AG 2017. All rights reserved.

Applications of continuous-time fractional order chaotic systems

2018Abdelaty A.M.Azar A.T.Book ChapterOuannas A.Radwan A.G.Vaidyanathan S.

The study of nonlinear systems and chaos is of great importance to science and engineering mainly because real systems are inherently nonlinear and linearization is only valid near the operating point. The interest in chaos was increased when Lorenz accidentally discovered the sensitivity to initial condition during his simulation work on weather prediction. When a nonlinear system is exhibiting deterministic chaos, it is very difficult to predict its response under external disturbances. This behavior is a double-edged weapon. From a control and synchronization point of view, this proposes a challenge. On the other hand, from a communications and encryption perspective, this provides a higher level of security. This chapter is a survey of the recent contributions in engineering applications of fractional order chaotic continuous-time systems. The applications include but not limited to: communication and encryption, FPGA implementations, synchronization and control, modeling of electric motors, and biomedical applications. © 2018 Elsevier Inc. All rights reserved.

Generalized synchronization of different dimensional integer-order and fractional order chaotic systems

2017Azar A.T.Book ChapterOuannas A.Radwan A.G.Ziar T.

In this work different control schemes are proposed to study the problem of generalized synchronization (GS) between integer-order and fractionalorder chaotic systems with different dimensions. Based on Lyapunov stability theory of integer-order differential systems, fractional Lyapunov-based approach and nonlinear controllers, different criterions are derived to achieve generalized synchronization. The effectiveness of the proposed control schemes are verified by numerical examples and computer simulations. © Springer International Publishing AG 2017. All rights reserved.

Generalized synchronization of different dimensional integer-order and fractional order chaotic systems

2017Azar A.T.JournalOuannas A.Radwan A.G.Ziar T.

In this work different control schemes are proposed to study the problem of generalized synchronization (GS) between integer-order and fractional order chaotic systems with different dimensions. Based on Lyapunov stability theory of integer-order differential systems, fractional Lyapunov-based approach and nonlinear controllers, different criterions are derived to achieve generalized synchronization. The effectiveness of the proposed control schemes are verified by numerical examples and computer simulations. © Springer International Publishing AG 2017.