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Stability analysis of fractional-order complex-valued neural networks with time delays. (English) Zbl 1353.34098

Summary: In this paper, we consider the problem of stability analysis of fractional-order complex-valued Hopfield neural networks with time delays, which have been extensively investigated. Moreover, the fractional-order complex-valued Hopfield neural networks with hub structure and time delays are studied, and two types of fractional-order complex-valued Hopfield neural networks with different ring structures and time delays are also discussed. Some sufficient conditions are derived by using stability theorem of linear fractional-order systems to ensure the stability of the considered systems with hub structure. In addition, some sufficient conditions for the stability of considered systems with different ring structures are also obtained. Finally, three numerical examples are given to illustrate the effectiveness of our theoretical results.

MSC:

34K37 Functional-differential equations with fractional derivatives
82C32 Neural nets applied to problems in time-dependent statistical mechanics
34K20 Stability theory of functional-differential equations
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