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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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