Spatiotemporal pattern formation and selection induced by cross-diffusion in a cancer growth model with Allee effect.

In this paper, we study the temporal and spatiotemporal dynamics of a cancer growth model with the Allee effect. For the temporal model, we first prove its well-posedness and analyze its rich local bifurcations, such as the transcritical bifurcation, the saddle-node bifurcation, the Hopf bifurcation, and the Bogdanov-Takens bifurcation. For the diffusion system, we first prove that cross-diffusion is a key mechanism for the formation of spatial patterns.