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Turing and Hopf Bifurcation in a Diffusive Tumor-immune Model
  
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KeyWord:Tumor-immune model; Diffusion; Hopf bifurcation; Turing bifurcation; Stability
Author NameAffiliation
Jingnan Wang Department of Applied mathematics, Harbin University of Science and Technology, Harbin, Heilongjiang 150080, China 
Shengnan Liu Department of Applied mathematics, Harbin University of Science and Technology, Harbin, Heilongjiang 150080, China 
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Abstract:
      In order to understand the effect of the diffusion reaction on the interaction between tumor cells and immune cells, we establish a tumor-immune reaction diffusion model with homogeneous Neumann boundary conditions. Firstly, we investigate the existence condition and the stability condition of the coexistence equilibrium solution. Secondly, we obtain the sufficient and necessary conditions for the occurrence of Turing bifurcation and Hopf bifurcation. Thirdly, we perform some numerical simulations to illustrate the complex spatiotemporal patterns near the bifurcation curves. Finally, we explain spatiotemporal patterns in the diffusion action of tumor cells and immune cells.