Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays

Ping Bi, Shigui Ruan, Xinan Zhang

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical values and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations.

Original languageEnglish (US)
Pages (from-to)23101
Number of pages1
JournalChaos (Woodbury, N.Y.)
Volume24
Issue number2
DOIs
StatePublished - Jun 1 2014

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immune systems
Immune system
Immune System
Tumors
Tumor
tumors
Hopf bifurcation
Oscillation
oscillations
Cell
Cell Growth Processes
effectors
Interaction
Cells
Hopf Bifurcation
Critical value
Neoplasms
Cell growth
interactions
Asymptotic stability

ASJC Scopus subject areas

  • Medicine(all)

Cite this

Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays. / Bi, Ping; Ruan, Shigui; Zhang, Xinan.

In: Chaos (Woodbury, N.Y.), Vol. 24, No. 2, 01.06.2014, p. 23101.

Research output: Contribution to journalArticle

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