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2018 | OriginalPaper | Chapter

On Investigation of Stability and Bifurcation of Neural Network with Discrete and Distributed Delays

Authors : Vasyl Martsenyuk, Igor Andrushchak, Andrii Sverstiuk, Aleksandra Klos-Witkowska

Published in: Computer Information Systems and Industrial Management

Publisher: Springer International Publishing

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Abstract

Paper presents our results dealing with qualitative investigation of neural network including discrete and distributed time delays. We use indirect method to get exponential decay rates of the model. Dynamic behavior is also investigated numerically when changing model parameters. As a result we get point attractors which transit to periodic ones when increasing absolute values of parameters.

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In (1) denotion \(\int {g(x(\theta ))d\theta }\) means \([\int {g_1(x(\theta ))d\theta },\int {g_2(x(\theta ))d\theta },...,\int {g_n(x(\theta ))d\theta }]^\top \in {\mathbb {R}}^n\).

We mean that functional \(\Phi : C[a,b]\rightarrow {\mathbb {R}}^1\) is “monotonically increasing” if \(f(t)\le g(t)\), \(t\in [a,b]\) imlies \(\Phi [f] \le \Phi [g]\).

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Title: On Investigation of Stability and Bifurcation of Neural Network with Discrete and Distributed Delays
Authors: Vasyl Martsenyuk
Igor Andrushchak
Andrii Sverstiuk
Aleksandra Klos-Witkowska
Publisher: Springer International Publishing
Book: Computer Information Systems and Industrial Management
Print ISBN: 978-3-319-99953-1

Electronic ISBN: 978-3-319-99954-8

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-99954-8_26

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