1-D maps, chaos and neural networks for information processing

An application of complex dynamics and chaos in neural networks to information processing is studied. Mathematical models based on piecewise-linear maps implementing basic functions of information processing via complex dynamics and chaos are discussed. Realizations of these models by neural networks are presented. In contrast to other methods of using neural networks and associative memory to store information, the information is stored in dynamical attractors such as limit cycles, rather than equilibrium points. Retrieval of information corresponds to getting the state into the basin of attraction of the attractor. We show that noise-corrupted information or partial information are sufficient to drive the state into the basin of attraction of the attractor, thus these systems exhibit the property of associative memory.