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Chemical Turing Patterns and Diffusive Instabilities

In: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

Author

Listed:
  • David J. Wollkind

    (Washington State University, Department of Mathematics)

  • Bonni J. Dichone

    (Gonzaga University, Department of Mathematics)

Abstract

The Brusselator activator-inhibitor reaction-diffusion model is considered and conditions deduced by a normal-mode linear stability analysis for the development of chemical Turing instabilities over a parameter range for which the dynamical system in the absence of diffusion would exhibit a stable homogeneous distribution. The effect the introduction of an immobilizer would have on such diffusive instabilities is also examined. The limitations of linear stability predictions of this sort are discussed and the results of a nonlinear stability analysis which will be treated in detail in later chapters are sketched for the Brusselator. In the problems similar normal-mode linear stability analyses of the Schnackenberg simplification of the Brusselator and a simplified version of the so-called CDIMA (Chlorine Dioxide Iodine Malonic Acid) chemical reaction-diffusion system are considered.

Suggested Citation

  • David J. Wollkind & Bonni J. Dichone, 2017. "Chemical Turing Patterns and Diffusive Instabilities," Springer Books, in: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, chapter 0, pages 167-186, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-73518-4_8
    DOI: 10.1007/978-3-319-73518-4_8
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