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Asymptotic behavior and effective boundaries forage-structured population models in aperiodically changing environment
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
##### Abstract [en]

Human activity and other events can cause environmental changes to the habitat of organisms. The environmental changes effect the vital rates for a population. In order to predict the impact of these environmental changes on populations, we use two different models for population dynamics. One simpler linear model that ignores environmental competition between individuals and another model that does not. Our population models take into consideration the age distribution of the population and thus takes into consideration the impact of demographics. This thesis generalize two theorems, one for each model, developed by Sonja Radosavljevic regarding long term upper and lower bounds of a population with periodic birth rate ; see [6] and [5]. The generalisation consist in including the case where the periodic part of the birth rate can be expressed with a finite Fourier series and also infinite Fourier series under some constraints. The old theorems only considers the case when the periodic part of the birth rate can be expressed with one cosine term. From the theorems we discover a connection between the frequency of oscillation and the effect on population growth. From this derived connection we conclude that periodical changing environments can have both positive and negative effects on the population.

2017. , p. 49
##### Keyword [en]
age-structure, time-dependency, environmental variability, upper and lower boundaries, periodic oscillations, logistic
##### National Category
Mathematical Analysis
##### Identifiers
ISRN: LiTH-MAT-EX--2016/09--SEOAI: oai:DiVA.org:liu-133632DiVA, id: diva2:1061767
##### Subject / course
Applied Mathematics
(English)
##### Examiners
Available from: 2017-01-03 Created: 2017-01-03 Last updated: 2017-01-03Bibliographically approved

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Cite
Citation style
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• vancouver
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Language
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