A New Fractional-Order Hyperchaotic System and Its Adaptive Tracking Control

We construct for the first time a fractional-order hyperchaotic system via the original integer-order system. The dynamical behavior of this fractional-order hyperchaotic system is investigated in detail using first approximation method and Lyapunov exponents. Next, an adaptive control strategy for the univariate controlled hyperchaotic system has been proposed. Also, the tracking performance is fully taken into account in numerous applications, for instance, tracking sinusoidal periodic signal, self-synchronization, and generalized synchronization of heterogeneous structure. Simulation results illustrate the validity and performability of the proposed adaptive tracking control scheme.

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Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416502229 ◽

2016 ◽

Vol 26 (13) ◽

pp. 1650222 ◽

Cited By ~ 23

Author(s):

A. M. A. El-Sayed ◽

A. Elsonbaty ◽

A. A. Elsadany ◽

A. E. Matouk

Keyword(s):

Fractional Order ◽

Initial Conditions ◽

Circuit Simulation ◽

Equilibrium Points ◽

Dynamical Behavior ◽

Phase Portraits ◽

Control Technique ◽

Order System ◽

Qualitative Behavior ◽

Hyperchaotic System

This paper presents an analytical framework to investigate the dynamical behavior of a new fractional-order hyperchaotic circuit system. A sufficient condition for existence, uniqueness and continuous dependence on initial conditions of the solution of the proposed system is derived. The local stability of all the system’s equilibrium points are discussed using fractional Routh–Hurwitz test. Then the analytical conditions for the existence of a pitchfork bifurcation in this system with fractional-order parameter less than 1/3 are provided. Conditions for the existence of Hopf bifurcation in this system are also investigated. The dynamics of discretized form of our fractional-order hyperchaotic system are explored. Chaos control is also achieved in discretized system using delay feedback control technique. The numerical simulation are presented to confirm our theoretical analysis via phase portraits, bifurcation diagrams and Lyapunov exponents. A text encryption algorithm is presented based on the proposed fractional-order system. The results show that the new system exhibits a rich variety of dynamical behaviors such as limit cycles, chaos and transient phenomena where fractional-order derivative represents a key parameter in determining system qualitative behavior.

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An Adaptive Tracking Control of Fractional-Order Chaotic Systems with Uncertain System Parameter

Mathematical Problems in Engineering ◽

10.1155/2011/521549 ◽

2011 ◽

Vol 2011 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Ping Zhou ◽

Rui Ding

Keyword(s):

Fractional Order ◽

Chaotic System ◽

Tracking Control ◽

System Parameter ◽

Chaotic Systems ◽

Reference Signal ◽

Uncertain System ◽

Uncertain Parameter ◽

Adaptive Tracking Control ◽

Adaptive Tracking

An adaptive tracking control scheme is presented for fractional-order chaotic systems with uncertain parameter. It is theoretically proved that this approach can make the uncertain parameter fractional-order chaotic system track any given reference signal and the uncertain system parameter is estimated through the adaptive tracking control process. Furthermore, the reference signal may belong to other integer-orders chaotic system or belong to different fractional-order chaotic system with different fractional orders. Two examples are presented to demonstrate the effectiveness of the proposed method.

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