Displaying similar documents to “A global attractor in a general diffusive food chain model.”

Periodic solutions of a three-species periodic reaction-diffusion system

Tiantian Qiao, Jiebao Sun, Boying Wu (2011)

Annales Polonici Mathematici

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We study a periodic reaction-diffusion system of a competitive model with Dirichlet boundary conditions. By the method of upper and lower solutions and an argument similar to that of Ahmad and Lazer, we establish the existence of periodic solutions and also investigate the stability and global attractivity of positive periodic solutions under certain conditions.

Temporally Interruptive Interaction Allows Mutual Invasion of Two Competing Species Dispersing in Space

Hiromi Seno (2010)

Mathematical Modelling of Natural Phenomena

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With a reaction-diffusion system, we consider the dispersing two-species Lotka-Volterra model with a temporally periodic interruption of the interspecific competitive relationship. We assume that the competition coefficient becomes a given positive constant and zero by turns periodically in time. We investigate the condition for the coexistence of two competing species in space, especially in the bistable case for the population dynamics without dispersion. We could find that the...

The speed of propagation for KPP type problems. I: Periodic framework

Henry Berestycki, François Hamel, Nikolai Nadirashvili (2005)

Journal of the European Mathematical Society

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This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of...

The logarithmic delay of KPP fronts in a periodic medium

François Hamel, James Nolen, Jean-Michel Roquejoffre, Lenya Ryzhik (2016)

Journal of the European Mathematical Society

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We extend, to parabolic equations of the KPP type in periodic media, a result of Bramson which asserts that, in the case of a spatially homogeneous reaction rate, the time lag between the position of an initially compactly supported solution and that of a traveling wave grows logarithmically in time.

Non local reaction-diffusion equations modelling predator-prey coevolution.

Angel Calsina, Carles Perelló, Joan Saldaña (1994)

Publicacions Matemàtiques

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In this paper we examine a predator-prey system with a characteristic of the predator subject to mutation. The ultimate equilibrium of the system is found by Maynard-Smith et al. by the so-called ESS (Evolutionary Stable Strategy). Using a system of reaction-diffusion equations with non local terms, we conclude that ESS result for the diffusion coefficient tending to zero, without resorting to any optimization criterion.

Global stability of steady solutions for a model in virus dynamics

Hermano Frid, Pierre-Emmanuel Jabin, Benoît Perthame (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based...

Pattern Formation Induced by Time-Dependent Advection

A. V. Straube, A. Pikovsky (2010)

Mathematical Modelling of Natural Phenomena

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We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators,...