Date/Time
Date(s) - 06/03/2024
10:30 am - 11:20 am

Location: HH 312

Speaker: Dr. Gail Wolkowicz

Title:   Deriving and Analyzing Discrete Planar Models with Applications in Biology

Abstract:
 After reviewing different strategies for deriving multi-species discrete mathematical models, a new strategy is described and then used to derive a predator-prey model and a model of competition between two populations.  Phase-plane analysis is explained.  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 the next-iterate operator associated with the nullclines and their associated root-curves is introduced.   This provides an elementary approach that can be applied to analyze discrete planar models.  A standalone GUI to obtain augmented phase portraits will be demonstrated and is available at https://github.com/sabrinaheike/AugmentedPhasePortrait/tree/main

This is joint work with Sabrina Streipert now an Assistant Professor at the University of Pittsburgh based on:
Sabrina H. Streipert and Gail S. K. Wolkowicz, “ An augmented phase plane approach for discrete planar maps: Introducing next-iterate operators ,“ Mathematical Biosciences, 355, 108924, 19 pgs. 2023. https://doi.org/10.1016/j.mbs.2022.108924
and
S. H. Streipert and G. S. K. Wolkowicz. “A method to derive discrete population models,” In: Advances in Discrete Dynamical Systems, Difference Equations and Applications, eds: S. Elaydi, M.R.S. Kulanovic, & S. Kalabusic, Springer Proceedings in Mathematics & Statistics 416,473–494, Springer, (2023). https://doi.org/10.1007/978-3-031-25225-9_22

The App on Github is being developed by Victoria Ralph, an undergraduate at McMaster, under the joint supervision of Sabrina Streipert and Gail Wolkowicz for her Honours Health Science Thesis.