Displaying similar documents to “Dynamics and patterns of an activator-inhibitor model with cubic polynomial source”

Growth of heterotrophe and autotrophe populations in an isolated terrestrial environment

Piotr Paweł Szopa, Monika Joanna Piotrowska (2011)

Applicationes Mathematicae

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We consider the model, proposed by Dawidowicz and Zalasiński, describing the interactions between the heterotrophic and autotrophic organisms coexisting in a terrestrial environment with available oxygen. We modify this model by assuming intraspecific competition between heterotrophic organisms. Moreover, we introduce a diffusion of both types of organisms and oxygen. The basic properties of the extended model are examined and illustrated by numerical simulations.

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...

Diffusion and cross-diffusion in pattern formation

Wei-Ming Ni (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as 2 × 2 systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.

Viral infection model with diffusion and state-dependent delay: a case of logistic growth

Rezounenko, Alexander V.

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We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe...

On a Model of Leukemia Development with a Spatial Cell Distribution

A. Ducrot, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

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In this paper we propose a mathematical model to describe the evolution of leukemia in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous medium. We show the existence of two stationary solutions, one of them corresponds to the normal case and another one to the pathological case. The leukemic state appears as a result of a bifurcation when the normal state loses its stability. The critical conditions of leukemia development are determined by...

Influence of Vibrations on Convective Instability of Reaction Fronts in Porous Media

H. Aatif, K. Allali, K. El Karouni (2010)

Mathematical Modelling of Natural Phenomena

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The aim of this paper is to study the effect of vibrations on convective instability of reaction fronts in porous media. The model contains reaction-diffusion equations coupled with the Darcy equation. Linear stability analysis is carried out and the convective instability boundary is found. The results are compared with direct numerical simulations.

Pattern Formation of Competing Microorganisms in Sediments

Y. Schmitz, M. Baurmann, B. Engelen, U. Feudel (2010)

Mathematical Modelling of Natural Phenomena

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We present a three species model describing the degradation of substrate by two competing populations of microorganisms in a marine sediment. Considering diffusion to be the main transport process, we obtain a reaction diffusion system (RDS) which we study in terms of spontaneous pattern formation. We find that the conditions for patterns to evolve are likely to be fulfilled in the sediment. Additionally, we present simulations that are consistent with experimental data from the literature....