scholarly journals Controlling Chaos for a Fractional-Order Discrete System

2020 ◽  
Vol 1 ◽  
pp. 263-269
Author(s):  
Luis Alberto Quezada-Tellez ◽  
Luis Franco-Perez ◽  
Guillermo Fernandez-Anaya
Keyword(s):  
Fractional Order ◽  
Discrete System ◽  
Controlling Chaos

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

Hidden attractors in a new fractional–order discrete system: Chaos, complexity, entropy, and control

2020 ◽  
Vol 29 (5) ◽  
pp. 050504 ◽  
Author(s):  
Adel Ouannas ◽  
Amina Aicha Khennaoui ◽  
Shaher Momani ◽  
Viet-Thanh Pham ◽  
Reyad El-Khazali
Keyword(s):  
Fractional Order ◽  
Discrete System ◽  
Hidden Attractors ◽  
And Control

scholarly journals Improving the Asymptotic Properties of Discrete System Zeros in Fractional-Order Hold Case

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Cheng Zeng ◽  
Shan Liang ◽  
Yingying Su
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Discrete System ◽  
Order Term ◽  
Asymptotic Properties ◽  
Sampling Period ◽  
Approximate Expression ◽  
Sampled Data ◽  
Form Representation ◽  
Time Systems

Remarkable improvements in the asymptotic properties of discrete system zeros may be achieved by properly adjusted fractional-order hold (FROH) circuit. This paper analyzes asymptotic properties of the limiting zeros, as the sampling periodTtends to zero, of the sampled-data models on the basis of the normal form representation of the continuous-time systems with FROH. Moreover, when the relative degree of the continuous-time system is equal to one or two, an approximate expression of the limiting zeros for the sampled-data system with FROH is also given as power series with respect to a sampling period up to the third-order term. And, further, the corresponding stability conditions of the sampling zeros are discussed for fast sampling rates. The ideas of the paper here provide a more accurate approximation for asymptotic zeros, and certain known achievements on asymptotic behavior of limiting zeros are shown to be particular cases of the results presented.

CONTROLLING CHAOS IN A STATE-DEPENDENT NONLINEAR SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1111-1119 ◽  
Author(s):  
TAKUJI KOUSAKA ◽  
TETSUSHI UETA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
Dynamical System ◽  
Nonlinear System ◽  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Discrete System ◽  
Nonlinear Dynamical System ◽  
Nonlinear Dynamical ◽  
Controlling Chaos ◽  
State Dependent ◽  
General Method

In this paper, we propose a general method for controlling chaos in a nonlinear dynamical system containing a state-dependent switch. The pole assignment for the corresponding discrete system derived from such a nonsmooth system via Poincaré mapping works effectively. As an illustrative example, we consider controlling the chaos in the Rayleigh-type oscillator with a state-dependent switch, which is changed by the hysteresis comparator. The unstable one- and two-periodic orbits in the chaotic attractor are stabilized in both numerical and experimental simulations.

scholarly journals Controlling chaos through growth rate adjustment

2002 ◽  
Vol 7 (3) ◽  
pp. 191-199 ◽  
Author(s):  
Weihong Huang
Keyword(s):  
Growth Rate ◽  
Theoretical Analysis ◽  
Computer Simulations ◽  
Discrete System ◽  
Fast Growth ◽  
Controlling Chaos ◽  
Controlling Mechanism ◽  
Rate Adjustment ◽  
Effectiveness And Efficiency ◽  
Fast Growth Rate

An extremely fast growth-rate controlling mechanism has been developed to stabilize a discrete system. Theoretical analysis and computer simulations have been provided to show the effectiveness and efficiency of this new mechanism in practice.

scholarly journals Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ibtissem Talbi ◽  
Adel Ouannas ◽  
Amina-Aicha Khennaoui ◽  
Abdelhak Berkane ◽  
Iqbal M. Batiha ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete System ◽  
Chaotic Systems ◽  
Difference Operator ◽  
Three Dimensional ◽  
Discrete Operator ◽  
Hybrid Scheme ◽  
Lyapunov Approach ◽  
Master System ◽  
Control And Synchronization

Abstract The paper investigates control and synchronization of fractional-order maps described by the Caputo h-difference operator. At first, two new fractional maps are introduced, i.e., the Two-Dimensional Fractional-order Lorenz Discrete System (2D-FoLDS) and Three-Dimensional Fractional-order Wang Discrete System (3D-FoWDS). Then, some novel theorems based on the Lyapunov approach are proved, with the aim of controlling and synchronizing the map dynamics. In particular, a new hybrid scheme is proposed, which enables synchronization to be achieved between a master system based on a 2D-FoLDS and a slave system based on a 3D-FoWDS. Simulation results are reported to highlight the effectiveness of the conceived approach.

scholarly journals Chaos Suppression in a Gompertz-like Discrete System of Fractional Order

2020 ◽  
Vol 30 (03) ◽  
pp. 2050049
Author(s):  
Marius-F. Danca ◽  
Michal Fečkan
Keyword(s):  
Lyapunov Exponent ◽  
Fractional Calculus ◽  
Numerical Integration ◽  
Fractional Order ◽  
Discrete System ◽  
Control Algorithm ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Discrete Fractional Calculus ◽  
Chaos Suppression

In this paper, we introduce the fractional-order variant of a Gompertz-like discrete system. The chaotic behavior is suppressed with an impulsive control algorithm. The numerical integration and the Lyapunov exponent are obtained by means of the discrete fractional calculus. To verify numerically the obtained results, beside the Lyapunov exponent, the tools offered by the 0-1 test are used.

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