Alban P.M. Tsui and Antonia J. Jones

Abstract. 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 dierent types of stimuli and under noise. This articial neural system has a strong dynamical parallel to Freeman's observed biological phenomenon.

Figure 1

Iterative feedforward network with delayed connections The chaotic system in this paper is simply a 2 inputs 2 outputs feedforward network as the main building block. The feedforward network is trained on a chaotic map, in this case the Ikeda map. By feeding the outputs back into the inputs of this network, we construct a chaotic iterative neural network. Then we attach a delayed feedback module as shown in the diagram, Figure 1. This module performs simply the "delayed feedback control" for this chaotic network. And this control module switches on automatically whenever an external simulus is presented into the input. Then we can study the response of this network by observing the output signals. In fact, a wide variety neural responses can be seen by feeding different stimuli into the network. Such response behaviour (periodic dynamical behaviour) seems to be some stabilised unstable periodic orbits originally embedded within the chaotic attractor (with no stimulus present and no control).

References

• Freeman, W. [1991] "The physiology of perception," Sci. Am. Feb, 34-41.
• Pyragas, K. [1992] "Continuous control of chaos by self- controlling feedback," Phys. Lett. A170, 421-428.

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