Electron. J. Differential Equations, Vol. 2017 (2017), No. 246, pp. 1-12.

Indirect method of exponential convergence estimation for neural network with discrete and distributed delays

Vasyl Martsenyuk

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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