Vasyl Martsenyuk
Abstract:
The purpose of this research is to develop method of calculation of
exponential decay rate for neural network model based on differential
equations with discrete and distributed delays. The method results
in quasipolynomial inequality allowing us to investigate qualitative
behavior of model in dependence on parameters. In such way it was
shown direct dependency in changes of exponential decay rate and minimal
threshold of distributed time delay.
An example of two-neuron network with four delays is given and
numerical simulations are performed to illustrate the obtained results.
It was shown numerically that distributed delays combined with discrete
delays narrow the interval of parameters admitting exponential convergence.
Submitted May 2, 2017. Published October 6, 2017.
Math Subject Classifications: 68T10, 34K20, 34K60, 92B20.
Key Words: Neural network model; exponential decay rate; discrete delays;
distributed delays; delay differential equations.
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Vasyl Martsenyuk Department of Computer Science and Automatics Faculty of Mechanical Engineering and Computer Science University of Bielsko-Biala Willowa Str 2, 43-309 Bielsko-Biala, Poland email: vmartsenyuk@ath.bielsko.pl |
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