## Dynamics in binary neural networks with a finite number of patterns. I: General picture of the asynchronous zero temperature dynamics.(English)Zbl 0891.58032

Summary: We rigorously define and study the limiting dynamics for Pastur-Figotin-Hopfield models of neural networks with $$N$$ nodes and $$p$$ patterns in the (thermodynamic) limit $$N\to\infty$$, $$p\equiv \text{const}$$. We study local and global properties of this limiting dynamics.

### MSC:

 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 68Q80 Cellular automata (computational aspects)
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