Open AccessBifurcation in a Discrete-Time Piecewise Constant Dynamical System
Author(s) -
Chenmin Hou,
Sui Sun Cheng
Publication year - 2013
Publication title -
discrete dynamics in nature and society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.264
H-Index - 39
eISSN - 1607-887X
pISSN - 1026-0226
DOI - 10.1155/2013/492014
Subject(s) - piecewise , constant (computer programming) , bifurcation , quotient , scalable vector graphics , mathematics , combinatorics , pure mathematics , discrete mathematics , physics , mathematical analysis , computer science , quantum mechanics , nonlinear system , programming language , operating system
The study of recurrent neural networks with piecewise constant transition or control functions has attracted much attention recently because they can be used to simulate many physical phenomena. A recurrent and discontinuous two-state dynamical system involving a nonnegative bifurcation parameter is studied. By elementary but novel arguments, we are able to give a complete analysis on its asymptotic behavior when the parameter varies from 0 to . It is hoped that our analysis will provide motivation for further results on large-scale recurrent McCulloch-Pitts-type neural networks and piecewise continuous discrete-time dynamical systems
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