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Zbl 1181.34063
Wu, Huaiqin
Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions. (English)
[J] Inf. Sci. 179, No. 19, 3432-3441 (2009). ISSN 0020-0255

A general class of neural networks is studied in the case when the neuron activation functions are modeled by discontinuous functions with linear growth. First the author proves the existence of periodic solutions for such nets by means of Leray-Schauder alternative theorem. Sufficient condition for global asymptotic stability of the periodic solutions is obtained using the matrix theory and generalized Lyapunov approach. Two illustrative examples are considered as well.
[Angela Slavova (Sofia)]

MSC 2000:: *34D23 Global stability
92B20 General theory of neural networks
34C25 Periodic solutions of ODE
47N20 Appl. of operator theory to differential and integral equations
34A60 ODE with multivalued right-hand sides
34A36 Discontinuous equations

Keywords: neural networks; global asymptotic stability; periodic solutions; Lyapunov approach; differential inclusions

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