Nonlinear Dynamics and Stability of Analog Neural Networks

摘要

We review a number of recent results on the dynamics and stability of networks ofanalog (graded-response) neurons. Topics are motivated by practical issues of implementation, especially concerning the use of electronic circuits and multiprocessor computers to build fast, stable neural networks. Stability criteria for symmetrically connected networks are presented which generalize the famous results symmetric connection yields fixed points only to include neurons with time-delayed response as well as discrete-time dynamics with parallel updating. Example applications include long-range and nearest-neighbor two lattices with delayed lateral inhibition and analog associative memories with iterated-map dynamics. We also describe a small (3-neuron) electronic analog network that exhibits delay-induced chaos. Finally, analytical and numerical results are presented showing how lowering neuron gain can dramatically reduce the number of spurious attractors and thus improve the performance of an analog network.