Geodesic
Positive fixed point theorems arising from seeking steady states of neural networks
Mathematica Bohemica, Tome 135 (2010) no. 1, pp. 99-112

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Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The derivation is based on elementary analysis. However, it is hoped that our easy fixed point theorems have potential applications in exploring stationary states of similar biological network models.
Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The derivation is based on elementary analysis. However, it is hoped that our easy fixed point theorems have potential applications in exploring stationary states of similar biological network models.
DOI : 10.21136/MB.2010.140686
Classification : 92B20
Keywords: positive fixed point; neural network; periodic solution; difference equation; discrete boundary condition; critical point theory 
Wang, Gen-Qiang; Cheng, Sui Sun. Positive fixed point theorems arising from seeking steady states of neural networks. Mathematica Bohemica, Tome 135 (2010) no. 1, pp. 99-112. doi: 10.21136/MB.2010.140686
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