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Multistability of neural networks with discontinuous activation function. (English) Zbl 1221.34131

Summary: The multistability is studied for two-dimensional neural networks with multilevel activation functions. It is shown that the system has \(n^{2}\) isolated equilibrium points which are locally exponentially stable, where the activation function has \(n\) segments. Furthermore, evoked by periodic external input, \(n^{2}\) periodic orbits which are locally exponentially attractive, can be found. These results are extended to \(k\)-neuron networks, which really enlarge the capacity of the associative memories. Examples and simulation results are used to illustrate the theory.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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