Conditions for wave-front instability of a propagating chemotaxic bacterial population

Using mathematical modeling, bacterial population front stability was studied for the case of nonlinear diffusion as well as bacteria chemotaxis. The conditions of transition from radial waves to fractal-type structures. The known Keller-Segel chemotaxis model is used, modified for nonlinear diffusion, when the diffusion coefficient is not a constant but function of bacteria and substrate concentration. As shown, the distinct fractal-type structure is formed only in a medium, where both chemotaxis and diffusion coefficients are small (D = 0.1 and v = 2.0). In such medium the bacterial front perturbations aren't 'dissipated' by diffusion and chemotaxis flows generated at bacteria and substrate concentrations' spatial gradients.