Parameter domains for generating spatial pattern: A comparison of reaction-diffusion and cell-chemotaxis models

Reaction-diffusion and cell-chemotaxis mechanisms have been widely used as models for biological pattern formation. Applications require the formation of specific patterns. Both mechanisms involve local reaction dynamics and diffusion. In addition, the cell-chemotaxis mechanism involves chemotactic movement in response to an external gradient. It has been considered that chemotaxis is like negative diffusion which has a destabilizing effect. In this paper, we use a general weakly nonlinear analysis and numerical simulations to divide the parameter space into different domains giving rise to specific classes of spatial patterns, namely, spots and stripes, compare the robustness and sensitivity of the different models, and discuss spatial patterns intermediate between stripes and spots. We show that chemotaxis is not always a destabilizing factor - it can also have positive diffusion effect.