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Abstract and Applied Analysis
Volume 2014, Article ID 723159, 12 pages
Research Article

Bifurcations of Tumor-Immune Competition Systems with Delay

Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China

Received 5 November 2013; Accepted 6 January 2014; Published 16 April 2014

Academic Editor: Kaifa Wang

Copyright © 2014 Ping Bi and Heying Xiao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.