#### Year

2021

#### Degree Name

Doctor of Philosophy

#### Department

School of Mathematics and Applied Statistics

#### Abstract

Population models are established to understand the description of population growth dynamics in an area or ecosystem. The use of maximum (carrying) capac-ity as a variable is deemed to be more realistic than a constant since the maximum population size may change because of some factors such as technology, economy and so on. Until now, many researchers have proposed various forms of popu-lation models, while the variable carrying capacity has begun to be widely used. However these variations, either for population or carrying capacity growth rate, have similar characteristics. Therefore qualitative and quantitative analysis can be done to the population models in a general form.

The purpose of this thesis is to examine population models involving a single or a system of ordinary differential equations, where the carrying capacity is set to be one of the state variables. Qualitative and quantitative solutions are analysed here. For human population, several carrying capacity models are introduced to verify population dynamics against actual data collected from the Food and Agricultural Organisation (FAO). In an ecological environment, Kolmogorov’s general population models with given assumptions are used to find exact solu-tions. Then a population harvesting term is added to these models to inspect steady state behaviour as a function of the harvesting values. The population models are also implemented in fisheries management. Fish population is har-vested by a control effort variable in order to gain maximum net profit. Then the model is modified by specifying the fish carrying capacity as a food source, where it is also harvested with a different control effort variable.

#### Recommended Citation

Zulkarnaen, Diny, Qualitative and Quantitative Analysis of Population Models with Variable Carrying Capacity, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2021. https://ro.uow.edu.au/theses1/1166

#### FoR codes (2020)

490102 Biological mathematics, 490103 Calculus of variations, mathematical aspects of systems theory and control theory, 490105 Dynamical systems in applications

**Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.**