Andò, A., De Reggi, S., Liessi, D. et al. (1 more author) (2023) A pseudospectral method for investigating the stability of linear population models with two physiological structures. Mathematical Biosciences and Engineering, 20 (3). pp. 4493-4515. ISSN 1547-1063
Abstract
The asymptotic stability of the null equilibrium of a linear population model with two physiological structures formulated as a first-order hyperbolic PDE is determined by the spectrum of its infinitesimal generator. In this paper, we propose a general numerical method to approximate this spectrum. In particular, we first reformulate the problem in the space of absolutely continuous functions in the sense of Carathéodory, so that the domain of the corresponding infinitesimal generator is defined by trivial boundary conditions. Via bivariate collocation, we discretize the reformulated operator as a finite-dimensional matrix, which can be used to approximate the spectrum of the original infinitesimal generator. Finally, we provide test examples illustrating the converging behavior of the approximated eigenvalues and eigenfunctions, and its dependence on the regularity of the model coefficients.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) |
Keywords: | bivariate collocation; infinitesimal generator; partial differential equations; stability of equilibria; physiologically structured populations |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 29 Jan 2024 10:33 |
Last Modified: | 29 Jan 2024 10:33 |
Published Version: | https://www.aimspress.com/article/doi/10.3934/mbe.... |
Status: | Published |
Publisher: | AIMS Press |
Identification Number: | 10.3934/mbe.2023208 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208323 |
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