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Qualitative analysis and synthesis of a class of neural networks. (English) Zbl 0664.34042

In the present paper we investigate the dynamic properties of a class of neural networks (which includes the Hopfield model as a special case) by studying the qualitative behavior of equilibrium points. Our results fall into one of two categories: one type of results pertains to analysis (e.g., stability properties of an equilibrium, asymptotic behavior of solutions, etc.) while the second type of result pertains to synthesis (e.g., the design of a neural network with prespecified equilibrium points which are asymptotically stable). Most (but not all) of the results presented herein are global. We demonstrate the applicability of our results by means of a specific example.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
92C05 Biophysics
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