Nonlinear dynamics and stability of analog neural networks

• Published in: Physica. D 1991-08, Vol.51 (1), p.234-247
• Main Authors: Marcus, C.M., Waugh, F.R., Westervelt, R.M.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Nonlinear dynamics and nonlinear dynamical systems; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/0167-2789(91)90236-3

We review a number of recent results on the dynamics and stability of networks of analog (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 result “symmetric connections ⇒ 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 2D 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.