Bifurcation analysis in models of tumor and immune system interactions

Dan Liu, Shigui Ruan, Deming Zhu

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The purpose of this paper is to present qualitative and bifurcation analysis near the degenerate equilibrium in models of interactions between lymphocyte cells and solid tumor and to understand the development of tumor growth. Theoretical analysis shows that these cancer models can exhibit Bogdanov-Takens bifurcation under sufficiently small perturbation of the system parameters whether it is vascularized or not. Periodic oscillation behavior and coexistence of the immune system and the tumor in the host are found to be influenced significantly by the choice of bifurcation parameters. It is also confirmed that bifurcations of codimension higher than 2 cannot occur at this equilibrium in both cases. The analytic bifurcation diagrams and numerical simulations are given. Some anomalous properties are discovered from comparing the vascularized case with the avascular case.

Original languageEnglish (US)
Pages (from-to)151-168
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume12
Issue number1
DOIs
StatePublished - Jul 2009

Fingerprint

Immune system
Immune System
Bifurcation Analysis
Tumors
Tumor
Bifurcation
Bogdanov-Takens Bifurcation
Tumor Growth
Lymphocytes
Qualitative Analysis
Bifurcation Diagram
Interaction
Small Perturbations
Coexistence
Codimension
Anomalous
Theoretical Analysis
Cancer
Oscillation
Numerical Simulation

Keywords

  • Bogdanov-Takens bifurcation
  • Lymphocyte
  • Oscillation
  • Saddle-node
  • Tumor
  • Vascularization

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Bifurcation analysis in models of tumor and immune system interactions. / Liu, Dan; Ruan, Shigui; Zhu, Deming.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 12, No. 1, 07.2009, p. 151-168.

Research output: Contribution to journalArticle

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