Stability and instability of equilibria of an equation of size structured population dynamics

Àngel Calsina; Manuel Sanchón

doi:https://doi.org/10.1016/S0022-247X(03)00464-5

Stability and instability of equilibria of an equation of size structured population dynamics

Àngel Calsina, Manuel Sanchón

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

19 Citations (Scopus)

Abstract

In this paper we consider a quasilinear equation with a nonlinear boundary condition modelling the dynamics of a biological population structured by size. We suppose vital rates depending on the total population. This hypothesis introduces some nonlinearities on the equation and on the boundary condition. We study the existence and uniqueness of solution of the initial value problem and the existence of stationary solutions. After we calculate the spectrum of the linearization at an equilibrium and we study its (local) stability. © 2003 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	435-452
Journal	Journal of Mathematical Analysis and Applications
Volume	286
DOIs	https://doi.org/10.1016/S0022-247X(03)00464-5
Publication status	Published - 15 Oct 2003

Keywords

Equilibria
Size-dependent population dynamics
Stability
Transcendental equation

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Calsina, À., & Sanchón, M. (2003). Stability and instability of equilibria of an equation of size structured population dynamics. Journal of Mathematical Analysis and Applications, 286, 435-452. https://doi.org/10.1016/S0022-247X(03)00464-5

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AB - In this paper we consider a quasilinear equation with a nonlinear boundary condition modelling the dynamics of a biological population structured by size. We suppose vital rates depending on the total population. This hypothesis introduces some nonlinearities on the equation and on the boundary condition. We study the existence and uniqueness of solution of the initial value problem and the existence of stationary solutions. After we calculate the spectrum of the linearization at an equilibrium and we study its (local) stability. © 2003 Elsevier Inc. All rights reserved.

KW - Equilibria

KW - Size-dependent population dynamics

KW - Stability

KW - Transcendental equation

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DO - https://doi.org/10.1016/S0022-247X(03)00464-5

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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