This dissertation presents several applications of the multi-scaling (multi-timing) technique to the analysis of both single and two species population models where the defining parameters vary slowly with time. Although exact solutions in such cases would be preferred, they are almost always impossible to obtain when slow variation is involved. Numerical solutions can be obtained in these cases, however they are often time consuming and offer limited insight into what is causing the behaviour we see in the solution. Here an approximation method is chosen as it gives an explicit analytic approximate expression for the solutions of such population models. The multi-scaling method was chosen because the defining parameters are varying slowly compared to the response of the system. This technique is well-established in the physical and engineering sciences literature; however, it has rarely been applied in the area of population modelling. All single species differential equation population models incorporate parameters which define the model - for example, the growth rate r and the carrying capacity k, for the Logistic model. For constant parameter values an exact solution may be found, giving the population as a function of time. However, for arbitrary time-varying parameters, exact solutions are rarely possible, and numerical solution techniques must be employed. Here we will demonstrate that for a Logistic model where the growth rate and carrying capacity both vary slowly with time, an analysis with multiple time scales leads to approximate closed form solutions that are explicit. These solutions prove to be valid for a range of parameter values and compare favourably with numerically generated ones.

Thesis (Ph.D.)--Tufts University, 1988. / Submitted to the Dept. of Engineering Design. Includes bibliographical references. Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph.D.)--Tufts University, 1998. / Adviser: Steven H. Levine. Submitted to the Dept. of Engineering Design. Includes bibliographical references (leaves 152-167). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph.D.)--Tufts University, 2001. / Adviser: Alva Couch. Submitted to the Dept. of Computer Science. Includes bibliographical references (leaves 231-234). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (M.Sc.)--York University, 2005. Graduate Programme in Earth and Space Science. / Typescript. Includes bibliographical references (leaves 130-140). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss &rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR11761

Thesis (Ph. D.)--Michigan State University. Measurement and Quantitative Methods , 2006. / Title from PDF t.p. (viewed on Mar. 30, 2009) Includes bibliographical references (p. 113-119). Also issued in print.

Thesis (M.S.)--University of Michigan, 1983.

Thesis (Ph. D.)--University of Texas at El Paso, 2008. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (M.S.)--University of Michigan, 1971.

Thesis (M.S.)--University of Michigan, 1983.