Merging traveling waves for the porous-Fisher's equation☆
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In this paper, the authors derived a nonlinear-diffusion porous-Fisher's equation for population dynamics using explicit traveling wave solutions, initially-separated, expanding populations are studied as they first coalesce.About:
This article is published in Applied Mathematics Letters.The article was published on 1995-07-01 and is currently open access. It has received 50 citations till now. The article focuses on the topics: Fisher's equation & Method of matched asymptotic expansions.read more
Citations
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Looking inside an invasion wave of cells using continuum models: Proliferation is the key
TL;DR: A two-species continuum model with logistic proliferation and a migration mechanism is developed here to simulate the chick-quail graft experiments and provide a means of looking at the processes occurring within the invasion wave.
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Reproducibility of scratch assays is affected by the initial degree of confluence: Experiments, modelling and model selection.
Wang Jin,Esha T. Shah,Catherine J. Penington,Scott W. McCue,Lisa K. Chopin,Matthew J. Simpson,Matthew J. Simpson +6 more
TL;DR: A suite of scratch assays in which the initial degree of confluence is vary (initial cell density) are analysed, indicating that the rate of re-colonisation is very sensitive to the initial density and that the Porous-Fisher model provides a better description of the experiments.
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Using Experimental Data and Information Criteria to Guide Model Selection for Reaction–Diffusion Problems in Mathematical Biology
TL;DR: This work uses Bayesian analysis and information criteria to demonstrate that model selection and model validation should account for both residual errors and model complexity, which are often overlooked in the mathematical biology literature.
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Revisiting the Fisher-Kolmogorov-Petrovsky-Piskunov equation to interpret the spreading-extinction dichotomy
TL;DR: This work revisit travelling wave solutions of the Fisher–KPP model and shows that these results provide new insight into travelling wave solution and the spreading–extinction dichotomy, using a combination of phase plane analysis, perturbation analysis and linearization.
References
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Pattern formation outside of equilibrium
Michael Cross,P. C. Hohenberg +1 more
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Book
Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
Book
Dynamics of curved fronts
TL;DR: In this paper, the Saffman-Taylor Finger is used to trace the shape of a curved flame growing from a supercooled liquid in a channel, and the shapes of a Needle Crystal Growing from a Supercooled Liquid.
Journal ArticleDOI
The regulation of inhomogeneous populations.
William Gurney,Roger M. Nisbet +1 more
TL;DR: It is shown that dispersal produced by wholly random motion is incapable of exerting any stabilizing influence, but that the introduction of a suitable non-linearity into the dispersal behaviour of a species whose characteristics are otherwise wholly linear can lead to stabilization under a wide range of conditions.