......................................................................

NJIT Mathematical Biology Seminar

Tuesday, April 29, 2008, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

......................................................................

Dynamic behavior of Pioner and Climax models

Yogesh Joshi

Department of Mathematical Sciences, NJIT

Modeling the evolution of populations of various species using nonlinear dynamics has become a well established strategy for analyzing and predicting behavior, and has led to some notable advances in ecological science research. Continuous as well as discrete dynamics have been incorporated into such models. I will begin the talk with a brief description of a general discrete model that subsumes almost all of the discrete population models currently in use. Results will be presented about fixed points and other important features, all of which identify important properties of the model, and also the actual systems which they represent. For example, fixed points correspond to ecological states of the populations that remain unchanged with time, and often correspond to possible long-time, steady state conditions.

Ecological Pioneer-Climax species, which usually refer to types of flora, have been studied for a great many years, and more recently have been extensively investigated using a variety of dynamical systems models, most of which have been limited to two-dimensional (two species) models. After discussing the general model, I will concentrate mainly on a three-dimensional Pioneer-Climax model, where there has been comparatively little work done from the dynamical systems viewpoint. More specifically, I will focus on three-dimensional hierarchical models, which have proved to be reasonably reliable predictors of Pioneer-Climax system evolution. I will describe an extensive theoretical and computational investigation of discrete three-dimension hierarchical Pioneer-Climax models, including an analysis of fixed and periodic points, bifurcations, and chaotic regimes, which will as far as possible be framed in an applied ecological context.