In this paper we introduce a conceptual model for vegetation patterns that generalizes the Klausmeier model for semi-arid ecosystems on a sloped terrain [23]. Our model not only incorporates downhill flow, but also linear or nonlinear diffusion for the water component. To relate the model to observations and simulations in ecology, we first consider the onset of pattern formation through a Turi...

We performed an extensive numerical study of pattern formation scenarios in the twodimensional Gray-Scott reaction-diffusion model. We concentrated on the parameter region in which there exists a strong separation of length and/or time scales. We found that the static one-dimensional autosolitons (stripes) break up into two-dimensional radially-symmetric autosolitons (spots). The traveling one-...

In this paper, we explore the emergence and direct interaction of two different types of dissipative structure in a single system: self-replicating chemical spot patterns and buoyancyinduced convection rolls. A new Lattice Boltzmann Model is developed, capable of simulating fluid flow, heat transport, and thermal chemical reactions, all within a simple, efficient framework. We report on a first...

Pattern formation in reaction-diffusion systems is of great importance in surface micropatterning [Grzybowski et al., Soft Matter 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al., Annu. Rev. Microbiol. 55, 105 (2001)], and in developmental biology [Barkai et al., FEBS Journal 276, 1196 (2009)]. In this work, we apply the lattice Boltzmann method to study pattern form...

The influence that intrinsic local-density fluctuations can have on solutions of mean-field reaction-diffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the presence of strong internal reaction noise. The dynamics of the Gray-Scott (GS) model [P. Gray and S. K. Scott, Chem. Eng. Sci. 38, 29 (1983); and ibid.39, 1087 (1...

The stability of a constant steady state in general reaction-diffusion activator-inhibitor model with nonlocal dispersal the activator or inhibitor is considered. It shown that Turing type instability and associated spatial patterns can be induced by fast slow diffusion, also causes but may not produce stable patterns. The existence nonconstant positive states throu...

Defining the roles of human CEACAMs during neutrophil responses to Neisseria 1 gonorrhoeae 2 3 Helen Sarantis and Scott D. Gray-Owen* 4 5 Department of Molecular Genetics, University of Toronto, Toronto, Ontario, Canada 6 7 Running Title: Dissecting roles of neutrophil CEA family members 8 9 *Address for Correspondence: 10 Dr. Scott D. Gray-Owen 11 University of Toronto 12 Department of Molecul...

This paper describes work carried out to investigate whether a classic simulated reaction-diffusion (RD) system could be used to control a ‘minimally cognitive’ animat during the course of a simple memory test. This test required the animat to remember an arbitrary signal and adapt its behaviour as a result. A further requirement was that the effects of the first signal be reversed by a second ...

A new criterion for the onset of spatio-temporal chaos arising in the Gray-Scott model is presented. This is based on the interrelationship of global bifurcating branches of stationary or periodic solutions with respect to the removal rate contained in the model, especially their locations of saddle-node points and the Hopf bifurcation point of a constant state play a key role. At the onset poi...