Nonlinear Size - Structured Population Models A

In this dissertation, some size-structured population models are studied.In Chapter 1, a quasilinear size-structured model that describes the dynamics of apopulation with n competing ecotypes is studied. Under the assumption that the vitalrates of each subpopulation depend on the total population due to competition, theconditions on the individual rates which guarantee competitive exclusion in the case ofclosed reproduction are provided. In particular, the results suggest that the ratio of thereproduction and mortality rates is a good measure to determine the winning ecotype.Meanwhile, in the case of open reproduction, the coexistence of all ecotypes is established.In Chapter 2, a model that describes the dynamics of the phytoplankton and zooplank-ton prey-predator system within the context of phytoplankton aggregation is considered.Existence-uniqueness results of the solution are established via a comparison principleand the upper-lower solution technique.In Chapter 3, a size-structured model that describes the dynamics of n-subpopulationswith nonlinear growth, reproduction and mortality rates is investigated. Existence anduniqueness results for the solutions are established. The existence of a compact globalattractor for the trajectories of the dynamical system defined by the solutions of thismodel is also obtained. In addition, two special cases under open reproduction arestudied and the asymptotic dynamics for these special cases are analyzed. 73BIOGRAPHICAL SKETCH Xubo Wang was born in September 1977, in Nanyang, Henan Province, China. Shewas admitted to Henan University in August 1994 and received her Bachelor of Science inMathematics Education in July 1998. Then she earned admittance to the graduate schoolat Southeast University in August 1998 and received her degree of Master of Science inApplied Mathematics in July 2001. In August 2001, she joined the Ph.D. program in theDepartment of Mathematics at the University of Louisiana at Lafayette. She completedthe requirements for the degree Doctor of Philosophy in July 2005.