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Huang, Gan; Cao, Jinde

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

Commun. Nonlinear Sci. Numer. Simul. 13, No. 10, 2279-2289 (2008).
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.

Cited in 23 Documents

MSC:

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

Keywords:

neural networks; multilevel function; activation function; multistability
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References:

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