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.
|Original language||English (US)|
|Number of pages||4|
|Journal||Doklady Akademii Nauk|
|State||Published - Sep 3 2004|