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I've found plenty of resources on Hopfield networks that use either discrete variables for both activation level and time or continuous variables for both activation level and time. Is it possible to construct a Hopfield neural network that uses a continuous variable for activation level and a discrete variable for time? If it is possible, can anyone offer resources and/or tips on how to construct one in software?

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I don't know, but here is the reverse: continuous time with binary neurons Orponen, P., & Šıma, J. (2000) –  Jeff Dec 18 '12 at 22:21

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up vote 5 down vote accepted

After doing some additional research, I think the answer is yes. It just means using a fixed timestep for the continuous-time activation equation (as described here). Since this is a differential equation, implementing it in software requires implementing a numerical integration method. I recommend the Exponential Euler Method as a starting point, because it's relatively simple and it's designed for differential equations of the sort that's used for the continuous Hopfield network.

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