Displaying similar documents to “Population Growth and Persistence in a Heterogeneous Environment: the Role of Diffusion and Advection”

Adaptive dynamics in logistic branching populations

Nicolas Champagnat, Amaury Lambert (2008)

Banach Center Publications

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The biological theory of adaptive dynamics proposes a description of the long-time evolution of an asexual population, based on the assumptions of large population, rare mutations and small mutation steps. Under these assumptions, the evolution of a quantitative dominant trait in an isolated population is described by a deterministic differential equation called 'canonical equation of adaptive dynamics'. In this work, in order to include the effect of genetic drift in this model, we...

Population changes as litmus paper of the socio-economic development level of small towns in Poland

Agnieszka Kwiatek-Sołtys (2015)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The main aim of the author was to analyse the population changes of small towns in Poland between 2002 and 2012. Small towns’ reaction to the global and regional demographic trends confirms their position between the rural areas and the urban municipalities. The differences between separate towns are significant, however those located within the metropolitan areas in Poland show a positive population dynamics, natural growth and migration balance net indexes. The image of small towns...

A parallel method for population balance equations based on the method of characteristics

Li, Yu, Lin, Qun, Xie, Hehu

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In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization. The application of the method of characteristics transform the higher dimensional population balance equation into a series of lower dimensional convection-diffusion-reaction equations which can be solved in a parallel way. Some numerical results are presented to show the accuracy and efficiency.

Large time behavior in a density-dependent population dynamics problem with age structure and child care

Vladas Skakauskas (2003)

Banach Center Publications

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Two asexual density-dependent population dynamics models with age-dependence and child care are presented. One of them includes the random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into the sum of two terms. The first presents death rate by the natural causes while the other describes the...

Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion

M. Alfaro, D. Hilhorst (2010)

Mathematical Modelling of Natural Phenomena

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In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.