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.
Supported by University of Bielsko-Biala.
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Notes
- 1.
In (1) denotion \(\int {g(x(\theta ))d\theta }\) means \([\int {g_1(x(\theta ))d\theta },\int {g_2(x(\theta ))d\theta },...,\int {g_n(x(\theta ))d\theta }]^\top \in {\mathbb {R}}^n\).
- 2.
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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The author would like to express his gratitude to the reviewer for the valuable comments.
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Martsenyuk, V., Andrushchak, I., Sverstiuk, A., Klos-Witkowska, A. (2018). On Investigation of Stability and Bifurcation of Neural Network with Discrete and Distributed Delays. In: Saeed, K., Homenda, W. (eds) Computer Information Systems and Industrial Management. CISIM 2018. Lecture Notes in Computer Science(), vol 11127. Springer, Cham. https://doi.org/10.1007/978-3-319-99954-8_26
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