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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:
34D05Asymptotic stability of ODE
92B20General theory of neural networks (mathematical biology)
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