Stability of fixed points and periodic orbits and bifurcations in analog neural networks

We consider some neural networks which have interesting oscillatory dynamics and analyze stability and bifurcation properties. The neurons are of the sigmoidal type (i.e., analog elements which have states in a real interval, X). The dynamics is discrete-time and synchronous. Thus, for an m-neuron network, it is given by iteration of a map F:X^m -> X^m. The study of such discrete-time continuum-state systems is motivated both by the difference equations which arise in numerical simulation of differentiable neural networks and independently by the possibility of constructing VLSI circuits with clocking techniques to implement such neural networks having prescribed fixed-points or periodic orbits.

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