Physical Sciences and Mathematics Commons^™

Computation Sequences For Series And Polynomials, Yiming Zhang

Electronic Thesis and Dissertation Repository

Approximation to the solutions of non-linear differential systems is very useful when the exact solutions are unattainable. Perturbation expansion replaces the system with a sequences of smaller problems, only the first of which is typically nonlinear. This works well by hand for the first few terms, but higher order computations are typically too demanding for all but the most persistent. Symbolic computation is thus attractive; however, symbolic computation of the expansions almost always encounters intermediate expression swell, by which we mean exponential growth in subexpression size or repetitions. A successful management of spatial complexity is vital to compute meaningful results. …

On Evolution Dynamics And Strategies In Some Host-Parasite Models, Liman Dai

Electronic Thesis and Dissertation Repository

In this thesis, we use mathematical models to study the problems about the evolution of hosts and parasites. Firstly, we study a within-host age-structured model with mutation and back mutation which is in the form of partial differential equations with double-infections by two strains of viruses. For the case when the production rates of viruses are gamma distributions, the PDE model can be transferred into an ODE one. Then, we analyze our model in two cases: one is without mutation, and the other is with mutation. In the first case, we prove that the two strains of viruses without mutation …

Modeling Leafhopper Populations And Their Role In Transmitting Plant Diseases., Ji Ruan

Electronic Thesis and Dissertation Repository

This M.Sc. thesis focuses on the interactions between crops and leafhoppers.

Firstly, a general delay differential equations system is proposed, based on the infection age structure, to investigate disease dynamics when disease latencies are considered. To further the understanding on the subject, a specific model is then introduced. The basic reproduction numbers $\cR_0$ and $\cR_1$ are identified and their threshold properties are discussed. When $\cR_0 < 1$, the insect-free equilibrium is globally asymptotically stable. When $\cR_0 > 1$ and $\cR_1 < 1$, the disease-free equilibrium exists and is locally asymptotically stable. When $\cR_1>1$, the disease will persist.

Secondly, we derive another general delay differential equations system to examine how different life stages of leafhoppers affect crops. The basic reproduction numbers $\cR_0$ is determined: when …

Ecological Constraints And The Evolution Of Cooperative Breeding, David Mcleod

Electronic Thesis and Dissertation Repository

Cooperative breeding is a social behaviour in which certain individuals will opt to delay or forgo their own reproduction in order to help other individuals. Cooperative breeding is one of the most conspicuous examples of cooperation in nature. However, theoretical understanding of why this behaviour occurs is lacking and contradictory. In this thesis, I examine the role played by ecological constraints on the emergence of cooperative breeding. Contrary to previous results, I find that ecological constraints do matter, provided the population dynamics are properly accounted for. I also examine the long-term evolutionary dynamics of cooperative breeding, and obtain the optimal …