Open AccessThe existence of codimension-two bifurcations in a discrete-time SIR epidemic model
Author(s) -
Xijuan Liu,
Peng Liu,
Yun Liu
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022187
Subject(s) - codimension , bifurcation , affine transformation , mathematics , stability (learning theory) , series (stratigraphy) , pure mathematics , discrete time and continuous time , statistical physics , physics , computer science , nonlinear system , statistics , quantum mechanics , paleontology , machine learning , biology
In this paper, we consider a discrete-time SIR epidemic model. Codimension-two bifurcations associated with 1:2, 1:3 and 1:4 strong resonances are analyzed by using a series of affine transformations and bifurcation theory. Numerical simulations are carried out to verify and illustrate these theoretical results. More precisely, two kinds of high-resolution stability phase diagrams are exhibited to describe how the system's complexity unfolds with control parameters varying.