Physical Sciences and Mathematics Commons^™

Population Dynamics And Bifurcations In Predator-Prey Systems With Allee Effect, Yanni Zeng

Electronic Thesis and Dissertation Repository

This thesis investigates a series of nonlinear predator-prey systems incorporating the Allee effect using differential equations. The main goal is to determine how the Allee effect affects population dynamics. The stability and bifurcations of the systems are studied with a hierarchical parametric analysis, providing insights into the behavioral changes of the population within the systems. In particular, we focus on the study of the number and distribution of limit cycles (oscillating solutions) and the existence of multiple stable states, which cause complex dynamical behaviors. Moreover, including the prey refuge, we examine how our method benefits the low-density animals and affects …

Study Of Behaviour Change And Impact On Infectious Disease Dynamics By Mathematical Models, Tianyu Cheng

Electronic Thesis and Dissertation Repository

This thesis uses mathematical models to study human behaviour changes' effects on infectious disease transmission dynamics. It centers on two main topics. The first concerns how behaviour response evolves during epidemics and the effects of adaptive precaution behaviour on epidemics. The second topic is how to build general framework models incorporating human behaviour response in epidemiological modelling.

In the first project, based on the fact that a fraction of the epidemiologically susceptible population is actually susceptible due to precautions, we present a novel perspective on understanding the infection force, incorporating human protection behaviours. This view explains many existing infection force …

Complex-Valued Approach To Kuramoto-Like Oscillators, Jacqueline Bao Ngoc Doan

Electronic Thesis and Dissertation Repository

The Kuramoto Model (KM) is a nonlinear model widely used to model synchrony in a network of oscillators – from the synchrony of the flashing fireflies to the hand clapping in an auditorium. Recently, a modification of the KM (complex-valued KM) was introduced with an analytical solution expressed in terms of a matrix exponential, and consequentially, its eigensystem. Remarkably, the analytical KM and the original KM bear significant similarities, even with phase lag introduced, despite being determined by distinct systems. We found that this approach gives a geometric perspective of synchronization phenomena in terms of complex eigenmodes, which in turn …