Turing and Hopf Bifurcation in a Diffusive Tumor-Immune Model (Journal of Nonlinear Modeling and Analysis, 2024)
In order to understand the effect of the diffusion reaction on the interaction between tumor cells and immune cells, we establish a tumor-immunereaction diffusion model with homogeneous Neumann boundary conditions.Firstly, we investigate the existence condition and the stability condition ofthe coexistence equilibrium solution. Secondly, we obtain the sufficient andnecessary conditions for the occurrence of Turing bifurcation and Hopf bifurcation. Thirdly, we perform some numerical simulations to illustrate the complexspatiotemporal patterns near the bifurcation curves. Finally, we explain spatiotemporal patterns in the diffusion action of tumor cells and immune cells.
Keywords: Tumor-immune model; Diffusion; Hopf bifurcation; Turing bifurcation; Stability.