The dynamics of hierarchical age-structured populations |
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Authors: | J. M. Cushing |
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Affiliation: | (1) Department of Mathematics, Interdisciplinary Program on Applied Mathematics, Building 89, University of Arizona, 85721 Tucson, AZ, USA |
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Abstract: | An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given. |
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Keywords: | Age-structured population dynamics McKendrick equations Hierarchical models Existence/uniqueness Asymptotic dynamics Global stability Intra-specific competition Cannibalism |
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