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A class of convergent neural network dynamics

✍ Scribed by Bernold Fiedler; Tomáš Gedeon

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
340 KB
Volume
111
Category
Article
ISSN
0167-2789

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✦ Synopsis

We consider a class of systems of differential equations in Nn which exhibits convergent dynamics. We find a Lyapunov function and show that every bounded trajectory converges to the set of equilibria. Our result generalizes the results of Cohen and Grossberg (1983) for convergent neural networks. It replaces the symmetry assumption on the matrix of weights by the assumption on the structure of the connections in the neural network.

We prove the convergence result also for a large class of Lotka-Volterra systems. These are naturally defined on the closed positive orthant. We show that there are no heteroclinic cycles on the boundary of the positive orthant for the systems in this class.

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