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Discussion of stability in a class of models on recurrent wavelet neural networks. (English) Zbl 1231.34086

Summary: Based on wavelet neural networks (WNNs) and recurrent neural networks (RNNs), a class of models on recurrent wavelet neural networks (RWNNs) is proposed. The new networks possess the advantages of WNNs and RNNs. In this paper, asymptotic stability of RWNNs is researched according to the Lyapunov theorem, and some theorems and formulae are given. The simulation results show the excellent performance of the networks in nonlinear dynamic system recognition.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
62M45 Neural nets and related approaches to inference from stochastic processes
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