## 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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### References:

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