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Exponential stability for stochastic jumping BAM neural networks with time-varying and distributed delays. (English) Zbl 1216.34081

Summary: We study the stability for a class of stochastic bidirectional associative memory (BAM) neural networks with jumps and time-varying and distributed delays. By using stochastic stability theory, the properties of a Brownian motion, the generalized Ito’s formula and the linear matrix inequalities technique, some novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or the zero solution. In particular, the activation functions considered in this paper are fairly general since they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. Also, the derivative of the time delays is not necessarily zero or smaller than 1. In summary, the results obtained in this paper extend and improve not only those with/without noise disturbances, but also with/without Markovian jump parameters. Finally, two interesting examples are provided to illustrate the theoretical results.

MSC:

34K50 Stochastic functional-differential equations
34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J27 Continuous-time Markov processes on discrete state spaces
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