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Order and localization in reaction-diffusion pattern

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  • Holloway, David M.
  • Harrison, Lionel G.

Abstract

The present work is concerned with two aspects of pattern formation: pattern localization and degree of pattern order. In reaction-diffusion models, there are three major effects. These stem from the reaction terms, the diffusion terms and the presence or absence of precursor gradients. Global analysis of reaction terms at late stages of pattern formation is at present unavailable. Therefore, we study the effect of the diffusion terms and of precursor gradients with numerical solution in two models: the Brusselator and the Gierer-Meinhardt. Differences in response to changes in the diffusion terms and the precursor gradients are related to contrasts between the nonlinear kinetics of the two models. These models both have Hill coefficient 2; effects of higher cooperativities have recently been discussed by Hunding and Engelhardt [1].

Suggested Citation

  • Holloway, David M. & Harrison, Lionel G., 1995. "Order and localization in reaction-diffusion pattern," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 222(1), pages 210-233.
    • Handle: RePEc:eee:phsmap:v:222:y:1995:i:1:p:210-233
    DOI: 10.1016/0378-4371(95)00202-2
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    References listed on IDEAS

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    1. Harman, C.E. & Meinhardt, K., 1972. "A computer system for treatment evaluation at the Community mental health center," American Journal of Public Health, American Public Health Association, vol. 62(12), pages 1596-1601.
    2. Gabriel Lipshitz, 1993. "The main approaches to measuring regional development and welfare," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 29(2), pages 163-181, June.
    3. Evans, George Heberton, 1954. "Geographical Differences in the Use of the Corporation in American Manufacturing in 1899," The Journal of Economic History, Cambridge University Press, vol. 14(2), pages 113-125, April.
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    Cited by:

    1. Iron, David & Ward, Michael J., 2001. "Spike pinning for the Gierer–Meinhardt model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(4), pages 419-431.

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