Numerical and qualitative stability analysis of ring and linear neural networks with a large number of neurons (Q2912235)
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scientific article; zbMATH DE number 6082517
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Numerical and qualitative stability analysis of ring and linear neural networks with a large number of neurons |
scientific article; zbMATH DE number 6082517 |
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14 September 2012
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neural networks
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delay differential matrix equations
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stability cone
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delay-independent stability
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Numerical and qualitative stability analysis of ring and linear neural networks with a large number of neurons (English)
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This paper considers a large number of ``neurons'' arranged in either a ring or line, each coupled to both of its nearest neighbours, but possibly in a delayed fashion. The dynamics are linear, so there is only one fixed point, the origin. Its stability depends on the strength of coupling between neighbouring neurons (which may be different for neurons to the right as opposed to to the left) and the values of any delays. Some theorems regarding the dependence of stability on these parameter values are proven, and numerical results given. Some of the results are given in the limit as the number of neurons tends to infinity.
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