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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Differential Equations
( Vol. 168 NO.1 / (2000))
Homoclinic Bifurcation in an $SIQR$ Model for Childhood Diseases
Lih-Ing Wu, Zhilan Feng,
Pages. 150-167
Abstract We consider a system of ODEs which describes the transmission dynamics of
childhood diseases. A center manifold reduction at a bifurcation point has the normal
form $x'=y, y'=axy+bx^2y+O(4)$, indicating a bifurcation of codimension
greater than two. A three-parameter unfolding of the normal form is studied to capture
possible complex dynamics of the original system which is subjected to certain
constraints on the state space due to biological considerations. It is shown that the
perturbed system produces homoclinic bifurcation
Contents 1. Introduction
2. The $SIQR$ model and singularities of the vector field
3. Unfolding analysis and homoclinic bifurcaton
Key words
Mathmatical Subject Classification