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Traveling wave solutions of a reaction–diffusion model for bacterial growth

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  • Mansour, M.B.A.

Abstract

In this paper, we consider a reaction–diffusion model for the bacterial growth. Mathematical analysis on the traveling wave solutions of the model is performed. This includes traveling wave analysis and numerical simulations of wave front propagation for a special case. Specifically, we show that such solutions exist only for wave speeds greater than some minimum speed giving wave with a sharp front. The minimum speed is estimated and the wave profile is calculated and compared with different numerical methods.

Suggested Citation

  • Mansour, M.B.A., 2007. "Traveling wave solutions of a reaction–diffusion model for bacterial growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 466-472.
    • Handle: RePEc:eee:phsmap:v:383:y:2007:i:2:p:466-472
    DOI: 10.1016/j.physa.2007.04.040
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    References listed on IDEAS

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    1. Golding, Ido & Kozlovsky, Yonathan & Cohen, Inon & Ben-Jacob, Eshel, 1998. "Studies of bacterial branching growth using reaction–diffusion models for colonial development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 260(3), pages 510-554.
    2. Mimura, Masayasu & Sakaguchi, Hideo & Matsushita, Mitsugu, 2000. "Reaction–diffusion modelling of bacterial colony patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 283-303.
    3. Matsushita, M & Wakita, J & Itoh, H & Watanabe, K & Arai, T & Matsuyama, T & Sakaguchi, H & Mimura, M, 1999. "Formation of colony patterns by a bacterial cell population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 190-199.
    4. Matsushita, M. & Wakita, J. & Itoh, H. & Ràfols, I. & Matsuyama, T. & Sakaguchi, H. & Mimura, M., 1998. "Interface growth and pattern formation in bacterial colonies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 249(1), pages 517-524.
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