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Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions. (English) Zbl 1181.34063
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.
MSC:
34D23Global stability of ODE
92B20General theory of neural networks (mathematical biology)
34C25Periodic solutions of ODE
47N20Applications of operator theory to differential and integral equations
34A60Differential inclusions
34A36Discontinuous equations
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