| In this thesis the age dynamics of a natural forest is modeled by the von-Foerster partial differential equation for the age density, while the seedlings density is obtained as a solution of an integro-differential equation. This seedlings density equation contains a small parameter, the ratio of seedlings re-establishment time and the life span of an average tree in the forest.; Several models are introduced that take into account various mortality curves and growth functions of trees, the dependence of seedlings carrying capacity on forest volume, and different types of seedlings re-establishment. Asymptotic, analytic and numerical methods are used to solve example problems. Existence and uniqueness of solutions and the convergence of numerical and asymptotic methods is proven for a class of models.; For a particular model the stability is examined, and a bifurcation point for the occurrence of oscillations is determined. |
