Control of chaos

In recent years, some studies on maintenance of chaos and control of chaos had been undertaken. The former has recently been experimentally demonstrated in a magnetomechanical system demonstrating intermittency. There is interest in such studies in view of the likelihood that Pathological destruction of chaotic behaviour possibly due to some underlying disease may be implicated in heart failure and brain seizers . 

Control of chaos has interest since one may want a system to be used for different purposes or under different conditions at different times. Such multipurpose flexibility is essential to higher life forms Ott, Grebegogi and Yorke (OGY) suggested a method [13] according to which one can convert a chaotic attractor to any one of a large number of possible attracting time-periodic perturbation of an available system parameter. 

It should be noted that chaos control can only be obtained if deterministic chaos is involved. In case of (i) chaotic laser (ii) diode (iii) hydrodynamic and magneto-elastic systems and (iv) more recently myocardial tissue, feedback algorithm has been successfully applied to stabilize periodic oscillations. Quite recently, in order to stabilize periodic behaviour in the chaotic regime of oscillatory B-Z reaction, Showalter [14] and co-workers (1998) applied proportional feedback mechanism. Feedback was applied to the system by perturbing the flow rate of cesium-bromate solutions in the reactor keeping the flow rate of malonic acid fixed in these experiments. This experimental arrangement helped the stabilization of periodic behaviour within the chaotic regime. 

Chaos in discrete neural networks has also received attention recently. Low dimensional strange attractors have been often observed in brain dynamics. Practical application to the treatment of epileptic foci has also been conjectured. 

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Below we show how the energy-optimal control of chaos can be solved via a statistical analysis of fluctuational trajectories of a chaotic system in the presence of small random perturbations. This approach is based on an analogy between the variational formulations of both problems [165] the problem of the energy-optimal control of chaos and the problem of stability of a weakly randomly perturbed chaotic attractor. One of the key points of the approach is the identification of the optimal control function as an optimal fluctuational force [165],... 

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A. G. Balanov, N. B. Janson, and E. Scholl. Period delayed feedback control of chaos Bifurcation analysis. Phys. Rev. E, 71 016222 (2005). 

In Chapter 12, special attention has been given to non-periodic oscillations of various types, including deterministic chaos and random motion (noise). Mathematical formalism, characterization and control of chaos have also been discussed. 

Control of chaos for the generation of new attractors with higher ethanol productivity. 

GonzSIez-Miranda JM (2004) Synchronization and control of chaos. An introduction for scientists and engineers. Imperial College Press, London... 

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