Discrete-time versus continuous-time models of neural networks
This paper considers the question of when a discretized version of a continuous-time (CT) system will have the same dynamical behavior as the original continuous-time system. Following a review of the status of the problem, the authors proceed to consider the general case of asymptotic consistency of the CT model and its associated discrete-time (DT) model. Specifically, let the CT system be given by the autonomous system of ordinary differential equations \(\dot x=F(x)\) and the corresponding DT model defined by \[ x(k+1)=x(k)+hF(x(k)). \] Conditions are given under which the DT model and the CT model have the same stable and unstable subspaces. Next, this general result is applied to four specific neural network models: (i) feedforward networks; (ii) symmetric networks; (iii) anti-symmetric networks; and (iv) circulant networks. These results generalize a number of results from the neural network literature, including those of Grossberg and Hopfield.
scientific article; zbMATH DE number 90310
scientific article