Open AccessBifurcation of a feed forward neural network with delay and application in image contrast enhancement
Author(s) -
Wen Long Wang,
Chunrui Zhang
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020021
Subject(s) - pitchfork bifurcation , mathematics , biological applications of bifurcation theory , phase portrait , singularity , bifurcation , hopf bifurcation , bifurcation diagram , computation , saddle node bifurcation , nonlinear system , mathematical analysis , codimension , artificial neural network , control theory (sociology) , computer science , physics , algorithm , control (management) , quantum mechanics , machine learning , artificial intelligence
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.