Feedback Control of Spatiotemporal Chaos in Photorefractive Ring Oscillator

We present the control and synchronization of spatiotemporal chaos in the photo-refractive ring oscillator systems with coupling technology. First, we realize the synchronization of spatiotemporal chaos in the two photorefractive ring oscillator systems via mutual coupling by choosing a suitable coupling strength. With the mutual coupling strength enlarging, the two mutual coupling photorefractive ring oscillator systems are controlled into periodic state, period number differs on account of the coupling strength and lattice coordinates. By increasing the coupling strength, the photorefractive ring oscillator is converted into period 8, subsequently it is converted into periods 4 and 2, periodic synchronization of the photorefractive ring oscillator systems is achieved at the same time. Calculation results show that period 1 is impossible by mutual coupling technology. Then, we investigate the influence of noise and parameter deviation on chaotic synchronization. We find that mutual coupling chaotic synchronization method can synchronize two chaotic systems with the weak noise and parameter deviation and has very good robustness. Given that the weak noise and parameter deviation have a slight effect on synchronization. Furthermore, we investigate two dimension control and synchronization of spatiotemporal chaos in the photorefractive ring osillator systems with coupling technology and get successful results. Mutual coupling technology is suitable in practical photorefractive ring oscillator systems.

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The coupled feedback control of spatiotemporal chaos based on the flocking algorithms

Acta Physica Sinica ◽

10.7498/aps.58.143 ◽

2009 ◽

Vol 58 (1) ◽

pp. 143

Author(s):

Yang Chao-Yu ◽

Tang Guo-Ning

Keyword(s):

Feedback Control ◽

Spatiotemporal Chaos

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EXPERIMENTAL EVIDENCE FOR SPATIOTEMPORAL STABILITY AND CONTROL OF A ONE-WAY OPEN CML

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402006254 ◽

2002 ◽

Vol 12 (12) ◽

pp. 2937-2944 ◽

Cited By ~ 1

Author(s):

TAKUYA IMAI ◽

KEIJI KONISHI ◽

HIDEKI KOKAME ◽

KENTARO HIRATA

Keyword(s):

Feedback Control ◽

Experimental Evidence ◽

Control Method ◽

Spatiotemporal Chaos ◽

Coupled Map Lattice ◽

Delayed Feedback Control ◽

Electronic Circuits ◽

Stability And Control ◽

Feedback Control Method ◽

And Control

We present an experimental evidence for spatiotemporal stability of a real one-way open coupled map lattice implemented by electronic circuits. Furthermore, it is shown that the decentralized delayed feedback control method can suppress the spatial instability and the spatiotemporal chaos in the coupled map lattice circuits.

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FEEDBACK CONTROL OF CHAOS IN SPATIOTEMPORAL SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127495000703 ◽

1995 ◽

Vol 05 (04) ◽

pp. 901-936 ◽

Cited By ~ 64

Author(s):

GANG HU ◽

ZHILIN QU ◽

KAIFEN HE

Keyword(s):

Feedback Control ◽

Nonlinear Systems ◽

Experimental Studies ◽

Lattice Models ◽

Dynamical Variable ◽

Spatiotemporal Chaos ◽

Coordinate Space ◽

Control Of Chaos ◽

Controlling Chaos ◽

Control Approach

This paper reviews the recent development in controlling and synchronizing chaos in spatiotemporal systems. In the first section we make a brief survey of the theoretical and experimental studies of controlling chaos in temporal systems. Section 2 is devoted to the dynamical variable feedback control approach by taking some temporal systems as examples. Some advantages of the variable feedback control over the parametric feedback control are emphasized. In Sec. 3, controlling and synchronizing spatiotemporal chaos in extended systems are presented by investigating the coupled map lattice models. In Sec. 4, we consider nonlinear systems described by partial differential equations, where momentum-space control by injecting feedback waves and coordinate-space control by injecting feedback signals at space points are used for successfully suppressing chaos and directing the system to certain regular motions.

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Nonlinear feedback control of spatiotemporal chaos in coupled map lattices

Discrete Dynamics in Nature and Society ◽

10.1155/s1026022697000289 ◽

1998 ◽

Vol 1 (4) ◽

pp. 283-305 ◽

Cited By ~ 10

Author(s):

Jin-Qing Fang ◽

M. K. Ali

Keyword(s):

Dynamical Systems ◽

Feedback Control ◽

Nonlinear Control ◽

Functional Method ◽

Spatiotemporal Chaos ◽

Numerical Results ◽

Coupled Map Lattices ◽

Nonlinear Feedback Control ◽

Nonlinear Feedback ◽

Control And Synchronization

We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed. Various numerical results of nonlinear control are given. We have not found any difficulty for study both of control and synchronization using nonlinear feedback functional method. The method can also be extended to time continuous dynamical systems as well as to society problems.

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Point-actuated feedback control of multidimensional interfaces

IMA Journal of Applied Mathematics ◽

10.1093/imamat/hxz031 ◽

2019 ◽

Vol 84 (6) ◽

pp. 1112-1142 ◽

Cited By ~ 1

Author(s):

Ruben J Tomlin ◽

Susana N Gomes

Keyword(s):

Feedback Control ◽

Control Strategies ◽

Liquid Films ◽

Travelling Wave ◽

Spatiotemporal Chaos ◽

Test Case ◽

Wide Range ◽

Local Observation ◽

State Observability ◽

Sivashinsky Equation

Abstract We consider the application of feedback control strategies with point actuators to multidimensional evolving interfaces in order to stabilize desired states. We take a Kuramoto–Sivashinsky equation as a test case; this equation arises in the study of thin liquid films, exhibiting a wide range of dynamics in different parameter regimes, including unbounded growth and full spatiotemporal chaos. The controls correspond physically to mass-flux actuators located in the substrate on which the liquid film lies. In the case of partial state observability, we utilize a proportional control strategy where forcing at a point depends only on the local observation. We find that point-actuated controls may inhibit unbounded growth of a solution, if the actuators are sufficient in number and in strength, and can exponentially stabilize the desired state. We investigate actuator arrangements, and find that the equidistant case is the most favourable for control performance, with a large drop in effectiveness for poorly arranged actuators. Proportional controls are also used to synchronize two chaotic solutions. When the interface is fully observable, we construct model-based controls using the linearization of the governing equation. These improve on proportional controls and are applied to stabilize non-trivial steady and travelling wave solutions.

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