Mathematical investigation of two dimensional pattern formation

  • Authors

    • Seyed Ali Madani Tonekaboni School of Mathematics, University of Waterloo, Ontario, Canada
    • Ali Shademani School of Mechanical Engineering, University of Tehran, Tehran, Iran
    2013-12-24
    https://doi.org/10.14419/ijbr.v2i1.1502

  • Abstract

    In this paper, one of the significant effects on two dimensional pattern formations of chemical reactions concerned with diffusion of species is investigated. Gray-Scott model is employed to study the effect of diffusion on reaction rate and distribution of the reactants. Nonlinear dimensionless partial differential equations of the problem are solved using explicit finite difference method. Contours of one agent are obtained for different parameter values and time dependencies of the patterns are investigated. Different time scales of the problem are also took into consideration.

     

    Keywords: Diffusion, finite difference method, Gray-Scott model, pattern formation, time scale.

  • References

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  • How to Cite

    Madani Tonekaboni, S. A., & Shademani, A. (2013). Mathematical investigation of two dimensional pattern formation. International Journal of Biological Research, 2(1), 1-5. https://doi.org/10.14419/ijbr.v2i1.1502

    Received date: 2013-11-11

    Accepted date: 2013-12-05

    Published date: 2013-12-24