Speaker: Gail Wolkowicz, McMaster University

Title: A Derivation Procedure for Multi-Species Discrete Population
Models and Analysis of Discrete Planar Models: Introducing the Augmented
Phase-Plane

Abstract:

After reviewing different strategies for deriving multi-species discrete
mathematical models, a new strategy is proposed and then used to derive a
predator--prey model and a model of competition between two populations.
It is shown why phase-plane analysis of planar maps has not been as useful
as it has been for planar systems of ordinary differential equations. To
rectify this issue we introduce the next-iterate operator associated with
the nullclines and their associated root-curves. The root-curves determine
on which side of the associated nullcline the next iterate lies.  How to
use the phase portrait augmented with the root-curves, to determine both
local and global  properties of discrete planar models, is demonstrated.
This provides an elementary approach that can be applied to help determine
properties of the dynamics of planar discrete models.