In this paper, we study the qualitative analysis of a reaction–diffusion system. The local stability of the trivial steady state, as well as the blow-up behavior of the solution are obtained. © 2004 Elsevier Ltd. All rights reserved. MSC: 35K20; 35B40

In this paper, a model composed of two Lotka-Volterra patches is considered. The system consists of two competing species X, Y and only species Y can diffuse between patches. It is proved that the system has at most two positive equilibria and then that permanence implies global stability. Furthermore, to answer the question whether the refuge is effective to protect Y , the properties of posit...

The new Information and Communication Technologies (ICT) give the possibility to have access to huge masses of information via varied supports (PC, PDA, Cell phone). Thus, to allow the traveller to find the information he is interested in, the personalization is the appropriate solution. In this article, we will propose a Personalized Multimodal Information Diffusion System (PMIDS) based on mul...

BACKGROUND AND PURPOSE The limbic system, relevant to memory and emotion, is an interesting subject of study in healthy and diseased individuals. It consists of a network of gray matter structures interconnected by white matter fibers. Although gray matter components of this system have been studied by using MR imaging, the connecting fibers have not been analyzed to the same degree. Cerebrospi...

In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary conditions at the interfaces to calculate the heat transport in this bounded system. We also consider the heat flux at the surface of the samle as boundary cond...

Non-linear waves of excitation are found in various biological, physical and chemical systems and are often accompanied by deformations of the medium. In this paper, we numerically study wave propagation in a deforming excitable medium using a twovariable reaction-diffusion system coupled with equations of continuum mechanics. We study the appearance and dynamics of different excitation pattern...

We have previously discussed the classical diffusive system of the bounded one-dimensional multitrap using the transfer-matrix method which is generally applied for studying the energy spectrum of the unbounded quantum Kronig-Penney multibarrier. It was shown, by this method, that for certain values of the relevant parameters the bounded multitrap array have unity transmission and a double-peak...

Patterns in reaction-diffusion systems generally consist of smooth traveling waves or of stationary, discontinuous Turing structures. Hybrid patterns that blend the properties of waves and Turing structures have not previously been observed. We report observation of dash waves, which consist of wave segments regularly separated by gaps, moving coherently in the Belousov-Zhabotinsky system dispe...