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Hopf Bifurcation in Abstract Semilinear Equations With Non-dense Domain and Applications to an Evolutionary Epidemiological Model of Influenza A Drift

Speaker

Shigui Ruan,Department of Mathematics, University of Miami

Time

2019.01.07 10:00-11:00

Venue

601, Pao Yue-Kong Library

Abstract

Normal form theory is very important and useful in simplifying the forms of equations restricted on the center manifolds in studying nonlinear dynamical problems. In this talk, using the center manifold theorem associated with the integrated semigroup theory, we introduce a Hopf bifurcation theorem and normal form theory for semilinear Cauchy problems in which the linear operator is not densely defined and is not a Hille-Yosida operator and present procedures to compute the Taylor’s expansion and normal form of the reduced system restricted on the center manifold. We then apply the main results and computation procedures to determine the direction of the Hopf bifurcation and stability of the bifurcating periodic solutions in a structured evolutionary epidemiological model of influenza A drift.