Displaying similar documents to “Pattern Formation of Competing Microorganisms in Sediments”

Irregularity of Turing patterns in the Thomas model with a unilateral term

Rybář, Vojtěch, Vejchodský, Tomáš

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In this contribution we add a unilateral term to the Thomas model and investigate the resulting Turing patterns. We show that the unilateral term yields nonsymmetric and irregular patterns. This contrasts with the approximately symmetric and regular patterns of the classical Thomas model. In addition, the unilateral term yields Turing patterns even for smaller ratio of diffusion constants. These conclusions accord with the recent findings about the influence of the unilateral term in...

Evolving morphogenetic fields in the zebra skin pattern based on Turing's morphogen hypothesis

Carlos Graván, Rafael Lahoz-Beltra (2004)

International Journal of Applied Mathematics and Computer Science

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One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm to the Young cellular...

Population Growth and Persistence in a Heterogeneous Environment: the Role of Diffusion and Advection

A. B. Ryabov, B. Blasius (2008)

Mathematical Modelling of Natural Phenomena

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The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible...