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Bifurcation Analysis of a Modified Tumor-immune System Interaction Model Involving Time Delay
- Source :
- Mathematical Modelling of Natural Phenomena. 12:120-145
- Publication Year :
- 2017
- Publisher :
- EDP Sciences, 2017.
-
Abstract
- We study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a reaction-diffusion system including time delay under the Neumann boundary conditions, and is based on Kuznetsov-Taylor's model. Choosing the delay parameter as a bifurcation parameter, we first show that Hopf bifurcation occurs. Second, we determine two properties of the periodic solution, namely its direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations. Furthermore, we discuss the effects of diffusion on the dynamics by analyzing a model with constant coefficients and perform some numerical simulations to support the analytical results. The results show that diffusion has an important effects on the dynamics of a mathematical model.
- Subjects :
- Hopf bifurcation
tumor immune system competition
Constant coefficients
delay differential equations
Differential equation
Applied Mathematics
periodic solutions
Delay differential equation
stability
reaction-diffusion system
01 natural sciences
Biological applications of bifurcation theory
010305 fluids & plasmas
symbols.namesake
Modeling and Simulation
0103 physical sciences
symbols
Neumann boundary condition
Applied mathematics
010301 acoustics
Center manifold
Bifurcation
Mathematics
Subjects
Details
- ISSN :
- 17606101
- Volume :
- 12
- Database :
- OpenAIRE
- Journal :
- Mathematical Modelling of Natural Phenomena
- Accession number :
- edsair.doi.dedup.....75dc193b8170f0a08d20ba1f3eee0eb1