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Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks
| Content Provider | MDPI |
|---|---|
| Author | Boykov, Ilya Roudnev, Vladimir Boykova, Alla |
| Copyright Year | 2022 |
| Description | A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems. We review here our study on an approximate solution of the Fredholm integral equation, and linear and nonlinear singular and hypersingular integral equations, using a continuous method for solving operator equations. This method assumes that the original system is associated with a Cauchy problem for systems of ordinary differential equations on Hopfield neural networks. We present sufficient conditions for the Hopfield networks’ stability defined via coefficients of systems of differential equations. |
| Starting Page | 2207 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math10132207 |
| Journal | Mathematics |
| Issue Number | 13 |
| Volume Number | 10 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2022-06-24 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Hopfield Neural Network Singular Hypersingular Integral Equations Nonlinear Differential Equations Stability Cauchy Problem Continuous Method |
| Content Type | Text |
| Resource Type | Article |
