Bifurcation Study and Turing Instability in a Diffusive Cell Polarization Model with Source and Loss Terms

In this paper, we study the spatiotemporal dynamics in a diffusive cell polarization model with source and loss terms under zero flux boundary conditions. Firstly, we investigate the stability of the positive equilibrium and the existence of Hopf bifurcation for the system without diffusion. Secondly, Turing instability and Turing bifurcation near the positive constant equilibrium are discussed for the diffusive system. Thirdly, the normal forms on the center manifold are given to determine the properties of Turing and Hopf bifurcations. Finally, numerical simulations are performed to illustrate our theoretical results.