Displaying similar documents to “Instabilities in a reaction diffusion model: spatially homogeneous and distributed systems.”

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.

On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors

M. A. Budroni, M. Rustici, E. Tiezzi (2010)

Mathematical Modelling of Natural Phenomena

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We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical...

A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

Hideki Murakawa (2009)

Kybernetika

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This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems....