For EDITORS

For READERS

All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Volume 9, Number 5, 2019, Pages 1855-1871                                                                DOI:10.11948/20180331
Dynamical analysis of a Lotka-Volterra learning-process model
Lingling Liu,Kewei Ding,Hebai Chen
Keywords:Saddle-node, transcritical bifurcation, picthfork bifurcation, Hopf bifurcation, Singular line segment.
Abstract:
      A Lotka-Volterra learning-process model was proposed by Monteiro and Notargiacomo in [{\it Commum. Nonlinear Sci. Numer. Simulat.} {\bf 47}(2017), 416-420] to approach learning process as an interplay between understanding and doubt. They studied the stability of the boundary equilibria and gave some numerical simulations but no further discussion for bifurcations. In this paper, we study the qualitative properties of the interior equilibria and a singular line segment completely. Moreover, we discuss their bifurcations such as transcritical, pitchfork, Hopf bifurcation on isolated equilibria and transcritical bifurcation without parameters on non-isolated equilibria. Finally, we also demonstrate these analytical theory by numerical simulations.
PDF      Download reader