Using neural networks for controlling chaos

A feed-forward backpropagating neural network is trained to achieve and maintain control of the unstable periodic orbits embedded in a chaotic attractor. The controlling algorithms used for training the network are based on the now standard scheme developed by Ott Grebogi and Yorke, including variants that utilize previous perturbations and/or delayedtime series data. 1. Introduction Chaotic systems are characterized by their sensitive dependence to small perturbations.In recent years. an abundance of theoretical and experimental research has been developedto capitalize on this fact and utilize it to control chaotic systems by applying very small,appropriately timed perturbations. Researchers have demonstrated the control of chaos in a host of physical systems ranging from lasers and electronic circuits to chemical and biological systems. For an excellent. recent review article see [1] and references therein.Neural networks are useful for a vast array of applications involving pattern and sym-hol recognition as well as for numerical computations. Recently. neural networks have beenemployed in the arena of dynamical systems as a tool for recognizing chaos in noisy experi