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Pattern Formation in a Bacterial Colony Model

Author

Listed:
  • Xinze Lian
  • Guichen Lu
  • Hailing Wang

Abstract

We investigate the spatiotemporal dynamics of a bacterial colony model. Based on the stability analysis, we derive the conditions for Hopf and Turing bifurcations. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by parameters in the model and find that the model dynamics exhibit a diffusion controlled formation growth to spots, holes and stripes pattern replication, which show that the bacterial colony model is useful in revealing the spatial predation dynamics in the real world.

Suggested Citation

  • Xinze Lian & Guichen Lu & Hailing Wang, 2014. "Pattern Formation in a Bacterial Colony Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:149801
    DOI: 10.1155/2014/149801
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    References listed on IDEAS

    as
    1. 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.
    2. Sheng Wang & Wenbin Liu & Zhengguang Guo & Weiming Wang, 2013. "Traveling Wave Solutions in a Reaction‐Diffusion Epidemic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Badoual, M. & Derbez, P. & Aubert, M. & Grammaticos, B., 2009. "Simulating the migration and growth patterns of Bacillus subtilis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 549-559.
    4. Yanuo Zhu & Yongli Cai & Shuling Yan & Weiming Wang, 2012. "Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-23, October.
    5. Yongli Cai & Caidi Zhao & Weiming Wang, 2013. "Spatiotemporal Complexity of a Leslie‐Gower Predator‐Prey Model with the Weak Allee Effect," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. Yuan Yuan & Hailing Wang & Weiming Wang, 2013. "The Existence of Positive Nonconstant Steady States in a Reaction: Diffusion Epidemic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Yongli Cai & Caidi Zhao & Weiming Wang, 2013. "Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-16, December.
    8. Yanuo Zhu & Yongli Cai & Shuling Yan & Weiming Wang, 2012. "Dynamical Analysis of a Delayed Reaction‐Diffusion Predator‐Prey System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    9. Yuan Yuan & Hailing Wang & Weiming Wang, 2013. "The Existence of Positive Nonconstant Steady States in a Reaction: Diffusion Epidemic Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, December.
    10. Sheng Wang & Wenbin Liu & Zhengguang Guo & Weiming Wang, 2013. "Traveling Wave Solutions in a Reaction-Diffusion Epidemic Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, April.
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