DYNAMICAL ANALYSIS OF A LOTKA-VOLTERRA LEARNING-PROCESS MODEL | Zendy

Lingling Liu | Zendy; Ke Ding | Zendy; Hebai Chen | Zendy

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DYNAMICAL ANALYSIS OF A LOTKA-VOLTERRA LEARNING-PROCESS MODEL

Author(s) -

Lingling Liu,

Ke Ding,

Hebai Chen

Publication year - 2019

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20180331

Subject(s) - pitchfork bifurcation , transcritical bifurcation , mathematics , bifurcation , nonlinear system , bogdanov–takens bifurcation , qualitative analysis , hopf bifurcation , stability (learning theory) , computer science , physics , qualitative research , social science , sociology , quantum mechanics , machine learning

A Lotka-Volterra learning-process model was proposed by Monteiro and Notargiacomo in [Commum. Nonlinear Sci. Numer. Simulat. 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.

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