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Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters. (English) Zbl 1176.92007

Summary: The stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jump parameters. The mixed delays include discrete and distributed time-delays, and the jump parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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