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PERIODIC RESPONSE TO EXTERNAL STIMULATION OF A CHAOTIC NEURAL NETWORK WITH DELAYED FEEDBACK

We construct a feedforward neural network so that when the outputs are fed back into the inputs and the system is iterated it behaves chaotically. We call this the "rest state". Suppose now that an input stimulus is added to one or more inputs. Following a biologically inspired model suggested by Freeman [1991], under these conditions we should want the behavior of the network to stabilize into an unstable periodic orbit of the original system. We call this the "retrieval behavior" since it is analogous to the act of recognition. Standard methods of chaos control, such as OGY for example, used to elicit the retrieval behavior would be inappropriate, since such methods involve calculations external to the system being controlled and can be considered unlikely in a biological neural network. Using a chaos control method originally suggested by Pyragas [1992] we show that retrieval behavior can occur as a result of delayed feedback and examine the variety of the responses that arise under different types of stimuli and under noise. This artificial neural system has a strong dynamical parallel to Freeman's observed biological phenomenon.