A numerical method for solving certain nonlinear integral equations arising in age-structured populations dynamics.
AuthorAlawneh, Zakaria Mohammad.
AdvisorCushing, Jim M.
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PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractIn this thesis we study the existence and stability of positive equilibrium of a general model for the dynamics of several interacting, age-structured population. We begin with the formulation and proof of a global existence theorem for the initial value problem. The proof of this theorem is used to develop an algorithm and a FORTRAN code for the numerical solution of initial value problems for the single species case. This computer program is used to study prototype models for the dynamics of a population whose fertility and mortality rates exhibit an "Allee effect". This is done from a bifurcation theoretic point of view, using the inherent net reproductive rate as a bifurcating parameter. An unstable "left" bifurcation is found. Multi-equilibria and various kinds of oscillations are studied as a function of r, the fertility window, and the nature of the density dependence.
Degree ProgramApplied Mathematics