Apm. Tsui et Aj. Jones, Periodic response to external stimulation of a chaotic neural network withdelayed feedback, INT J B CH, 9(4), 1999, pp. 713-722
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 Fr
eeman [1991], under these conditions we should want the behavior of the net
work to stabilize into an unstable periodic orbit of the original system. W
e call this the "retrieval behavior" since it is analogous to the act of re
cognition. Standard methods of chaos control, such as OGY for example, used
to elicit the retrieval behavior would be inappropriate, since such method
s involve calculations external to the system being controlled and can be c
onsidered unlikely in a biological neural network. Using a chaos control me
thod originally suggested by Pyragas [1992] we show that retrieval behavior
can occur as a result of delayed feedback and examine the variety of the r
esponses that arise under different types of stimuli and under noise. This
artificial neural system has a strong dynamical parallel to Freeman's obser
ved biological phenomenon.