# Positive fixed point theorems arising from seeking steady states of neural networks

Mathematica Bohemica (2010)

- Volume: 135, Issue: 1, page 99-112
- ISSN: 0862-7959

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topWang, Gen Qiang, and Cheng, Sui-Sun. "Positive fixed point theorems arising from seeking steady states of neural networks." Mathematica Bohemica 135.1 (2010): 99-112. <http://eudml.org/doc/38114>.

@article{Wang2010,

abstract = {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.},

author = {Wang, Gen Qiang, Cheng, Sui-Sun},

journal = {Mathematica Bohemica},

keywords = {positive fixed point; neural network; periodic solution; difference equation; discrete boundary condition; critical point theory; periodic solutions; difference equations; discrete boundary condition; critical point theory},

language = {eng},

number = {1},

pages = {99-112},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Positive fixed point theorems arising from seeking steady states of neural networks},

url = {http://eudml.org/doc/38114},

volume = {135},

year = {2010},

}

TY - JOUR

AU - Wang, Gen Qiang

AU - Cheng, Sui-Sun

TI - Positive fixed point theorems arising from seeking steady states of neural networks

JO - Mathematica Bohemica

PY - 2010

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 135

IS - 1

SP - 99

EP - 112

AB - 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.

LA - eng

KW - positive fixed point; neural network; periodic solution; difference equation; discrete boundary condition; critical point theory; periodic solutions; difference equations; discrete boundary condition; critical point theory

UR - http://eudml.org/doc/38114

ER -

## References

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