Research article

Bifurcation of a feed forward neural network with delay and application in image contrast enhancement

  • Received: 29 December 2018 Accepted: 05 June 2019 Published: 10 October 2019
  • This paper is concerned with how the singularity and delay in a feed forward neural network affect generic dynamics and bifurcations. By computation of Hopf-pitchfork point in a two-parameter nonlinear problem, the mode interactions in two parameters bifurcations with a single zero and a pair of imaginary roots are considered. The codimension two normal form with Hopf-pitchfork bifurcations are given. Then, the bifurcation diagrams and phase portraits are obtained by computing the normal form. Furthermore, we find some interesting dynamical behaviors of the original system, such as the coexistence of two unstable nontrivial equilibria and a pair of stable periodic orbits, which are verified both theoretically and numerically. Through numerical simulation, we also find that this model has a special signal enhancement property in Hopf bifurcation state. Using this feed-forward neural network, we show that the gray scale picture contrast is strongly enhanced even if this one is initially very small.

    Citation: Wenlong Wang, Chunrui Zhang. Bifurcation of a feed forward neural network with delay and application in image contrast enhancement[J]. Mathematical Biosciences and Engineering, 2020, 17(1): 387-403. doi: 10.3934/mbe.2020021

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  • This paper is concerned with how the singularity and delay in a feed forward neural network affect generic dynamics and bifurcations. By computation of Hopf-pitchfork point in a two-parameter nonlinear problem, the mode interactions in two parameters bifurcations with a single zero and a pair of imaginary roots are considered. The codimension two normal form with Hopf-pitchfork bifurcations are given. Then, the bifurcation diagrams and phase portraits are obtained by computing the normal form. Furthermore, we find some interesting dynamical behaviors of the original system, such as the coexistence of two unstable nontrivial equilibria and a pair of stable periodic orbits, which are verified both theoretically and numerically. Through numerical simulation, we also find that this model has a special signal enhancement property in Hopf bifurcation state. Using this feed-forward neural network, we show that the gray scale picture contrast is strongly enhanced even if this one is initially very small.
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    © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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