Large time behavior of the logistic age-structured population model in a changing environment

Article type: Research Article

Authors: Kozlov, Vladimir^a | Radosavljevic, Sonja^{a; *} | Wennergren, Uno^b

Affiliations: [a] Department of Mathematics, Linkoping University, 583-81 Linkoping, Sweden. E-mails: [email protected], [email protected] | [b] Department of Physics, Chemistry, and Biology, Linkoping University, 581-83 Linkoping, Sweden. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: Population growth is governed by many external and internal factors. In order to study their effects on population dynamics, we develop an age-structured time-dependent population model with logistic-type nonlinearity. We prove existence of a unique nonnegative bounded solution. Our main concern is to study asymptotic behavior of a solution in the general case, and especially for a periodic environment. We use the method of lower and upper solutions known in the theory of integral equations to formulate lower and upper boundaries of population density. In the periodic case, we discover a connection between the period of oscillation and its effect on population growth.

Keywords: Age-structure, time-variability, density-dependency, asymptotic behavior of solution

DOI: 10.3233/ASY-171409

Journal: Asymptotic Analysis, vol. 102, no. 1-2, pp. 21-54, 2017