Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 27, pp. 1-13.

Title: Hopf bifurcation for tumor-immune competition systems with delay

Authors: Ping Bi     (East China Normal Univ., Shanghai, China)
         Heying Xiao (East China Normal Univ., Shanghai, China)
 
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.