Ping Bi, Heying Xiao
Abstract:
In this article, a immune response system with
delay is considered, which consists of two-dimensional
nonlinear differential equations.
The main purpose of this paper is to explore the Hopf bifurcation
of a immune response system with delay. The general formula of the
direction, the estimation formula of period and stability of
bifurcated periodic solution are also given. Especially, the conditions
of the global existence of periodic solutions bifurcating from
Hopf bifurcations are given. Numerical simulations are carried out to
illustrate the the theoretical analysis and the obtained results.
Submitted October 9, 2013. Published January 14, 2014.
Math Subject Classifications: 34K18, 34K60, 92C37.
Key Words: Tumor-immune system; Hopf bifurcation; delay.
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Ping Bi Department of Mathematics, Shanghai Key Laboratory of PMMP East China Normal University 500 Dongchuan RD, Shanghai 200241, China email: pbi@math.ecnu.edu.cn |
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Heying Xiao Department of Mathematics, Shanghai Key Laboratory of PMMP East China Normal University 500 Dongchuan RD, Shanghai 200241, China email: hawcajok701@163.com |
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