# Introduction: Control and synchronization of chaos.

@article{Ditto1997IntroductionCA, title={Introduction: Control and synchronization of chaos.}, author={William L. Ditto and Kenneth Showalter}, journal={Chaos}, year={1997}, volume={7 4}, pages={ 509-511 } }

The hallmark of deterministic chaos, an extreme sensitivity to initial conditions, suggests that chaotic systems might be difficult if not impossible to control, since any perturbations used for control would grow exponentially in time. Indeed, this quite reasonable view was widely held until only a few years ago. Surprisingly, the basis for controlling chaos is provided by just this property, which allows carefully chosen, tiny perturbations to be used for stabilizing virtually any of the…

## 44 Citations

### Chaos control in mechanical systems

- Physics
- 2006

Chaos has an intrinsically richness related to its structure and, because of that, there are benefits for a natural system of adopting chaotic regimes with their wide range of potential behaviors.…

### CONTROLLING CHAOS IN A NONLINEAR PENDULUM

- Physics
- 2003

Chaotic behavior of dynamical systems offers a rich variety of orbits, which may be controlled by small perturbations in either a specific parameter of the system or a dynamical variable. Therefore,…

### Reliability of unstable periodic orbit based control strategies in biological systems.

- PhysicsChaos
- 2015

Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs.

### A New Method For Synchronization Of A Simple Chaotic systems

- Computer Science
- 2016

A new algorithm for controlling a class of simple chaotic system that contain only one nonlinear term that depends only on the nonlinear coupling term which makes the largest conditional Lyapunov exponents of the response system negative.

### Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics.

- PhysicsChaos
- 2003

It is found, through numerical computations and experiments with a chaotic electronic circuit, that with reasonable care the computed or measured entropy values can be preserved for a wide range of the filtering parameter.

### Feedback Synchronization using pole-Placement Control

- Computer Science, PhysicsInt. J. Bifurc. Chaos
- 2000

It is shown how two chaotic systems can be synchronized by applying small feedback perturbations to one of them by describing a feedback approach for synchronizing chaotic systems that is applicable in high dimensions.

### Control of nonlinear Dynamics: where do Models Fit in?

- MathematicsInt. J. Bifurc. Chaos
- 2000

Several control design techniques applied to nonlinear dynamics and chaos assume that a model of the uncontrolled dynamics is available. The extent to which the controller performance is influenced…

### Experimental Observation of Lag Synchronization in Coupled Chaotic Systems

- PhysicsInt. J. Bifurc. Chaos
- 2000

Measurements indicate that due to the influence of noise, lag synchronization appears to occur intermittently in time.

### Chaos and order in biomedical rhythms

- Biology
- 2005

An overview of nonlinear dynamics and chaos concepts useful for the analysis of biomedical system and some characteristics of normal and pathological responses are discussed.

## References

SHOWING 1-10 OF 25 REFERENCES

### Experimental control of chaos.

- PhysicsPhysical review letters
- 1990

It was demonstrated that one can convert the motion of a chaotic dynamical system to periodic motion by controlling the system about one of the many unstable periodic orbits embedded in the chaotic…

### Progress in the control of chaos

- Computer Science
- 1995

This review summarizes several of the key contributions made over the past 5 years to the control of chaotic dynamical systems and proposes control techniques for application to high- or infinite-dimensional systems.

### Controlling chaos using time delay coordinates.

- PhysicsPhysical review letters
- 1992

This chapter discusses controlling chaos using time delay coordinates, a new method of controlling a chaotic dynamical system by stabilizing one of the many unstable periodic orbits embedded in a chaotic attractor through only small time dependent perturbations in some accessible system parameter.

### Synchronization in chaotic systems.

- PhysicsPhysical review letters
- 1990

This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.

### Controlling chaos in the Belousov—Zhabotinsky reaction

- PhysicsNature
- 1993

DETERMINISTIC chaos is characterized by long-term unpredictability arising from an extreme sensitivity to initial conditions. Such behaviour may be undesirable, particularly for processes dependent…

### Stabilizing high-period orbits in a chaotic system: The diode resonator.

- PhysicsPhysical review letters
- 1991

The chaotic dynamics found in the diode resonator has been converted into stable orbits with periods up to 23 drive cycles long. The method used is a modification of that of Ott, Grebogi, and Yorke…

### Using small perturbations to control chaos

- PhysicsNature
- 1993

The extreme sensitivity of chaotic systems to tiny perturbations (the ‘butterfly effect’) can be used both to stabilize regular dynamic behaviours and to direct chaotic trajectories rapidly to a…

### Controlling cardiac chaos.

- BiologyScience
- 1992

By administering electrical stimuli to the heart at irregular times determined by chaos theory, the arrhythmia was converted to periodic beating and was stabilized to stabilize cardiac arrhythmias induced by the drug ouabain in rabbit ventricle.

### Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system.

- PhysicsPhysical review letters
- 1992

It is shown that complex periodic wave forms can be stabilized in the laser output intensity, indicating that this control technique may bewidely applicable to autonomous, higher-dimensional chaotic systems, including globally coupled arrays of nonlinear oscillators.