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Zbl 1136.34311
Liu, Yiguang; You, Zhisheng
Multi-stability and almost periodic solutions of a class of recurrent neural networks.
(English)
[J] Chaos Solitons Fractals 33, No. 2, 554-563 (2007). ISSN 0960-0779

The paper studies a class of reccurent neural networks described by the equations $$\dot x_i(t)=-a_i x_i(t)+\sum_{j=1}^n w_{ij} f(x_j(t))+c_i\,,\quad f(x)\in (-1,\,1)\quad i=1,\dots,n.$$ Using Lyapunov functions, a sufficient condition for the complete stability is obtained. On this base applying the Mawhin coincidence degree theory, many sufficient conditions guaranteeing the existence of at least one almost periodic solution are obtained. These conditions are derived for an arbitrary activation function $f$. Few simulations done by Matlab illustrate that the simulation results fit well the theoretic analysis.
[Ivan Ginchev (Varese)]
MSC 2000:
*34C27 Almost periodic solutions of ODE
34D20 Lyapunov stability of ODE
92B20 General theory of neural networks

Keywords: almost periodic solutions; stability; neural networks.

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