## Self-excitation of neurons leads to multiperiodicity of discrete-time neural networks with distributed delays.(English)Zbl 1227.93074

Summary: We investigate the interesting multiperiodicity of discrete-time neural networks with excitatory self-connections and distributed delays. Due to self-excitation of neurons, we construct $$2^N$$ closed regions in state space for $$N$$-dimensional networks and attain the coexistence of $$2^N$$ periodic sequence solutions in these closed regions. Meanwhile, we estimate exponential attracting domain for each periodic sequence solution and apply our results to discrete-time analogues of periodic or autonomous neural networks. Under self-excitation of neurons, numerical simulations are performed to illustrate the effectiveness of our results.

### MSC:

 93C55 Discrete-time control/observation systems 37N35 Dynamical systems in control 92B20 Neural networks for/in biological studies, artificial life and related topics
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### References:

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