18 citations · 26 across the 4 of their papers we have counts for
7 papers
An augmented phase plane approach for discrete planar maps: Introducing next-iterate operators
Sabrina H. Streipert, Gail S. K. Wolkowicz
The next-iterate operators and corresponding next-iterate root-sets and root-curves associated with the nullclines of a planar discrete map are introduced. How to augment standard…
Chaotic dynamics in a simple predator-prey model with discrete delay
Guihong Fan, Gail S. K. Wolkowicz
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that ha…
Growth on multiple interactive-essential resources in a self-cycling fermentor: An impulsive differential equations approach
Tyler Meadows, Gail S. K. Wolkowicz
We introduce a model of the growth of a single microorganism in a self-cycling fermentor in which an arbitrary number of resources are limiting, and impulses are triggered when the…
A qualitative study of an anaerobic food-web reveals the importance of hydrogen for microbial stability
Szymon Sobieszek, Gail S. K. Wolkowicz, Matthew J. Wade
The mathematical analysis of a three-tiered food-web describing anaerobic chlorophenol mineralisation has suggested the emergence of interesting dynamical behaviour through its spe…
Global analysis of a simplified model of anaerobic digestion and a new result for the chemostat
Tyler Meadows, Marion Weedermann, Gail S. K. Wolkowicz
A. Bornhöft, R. Hanke-Rauschenbach, and K. Sundmacher, [Nonlinear Dyn., 73 (2013), pp. 535-549] introduced a qualitative simplification to the ADM1 model for anaerobic digestion. W…
A Criterion for the Existence of Relaxation Oscillations with Applications to Predator-Prey Systems and an Epidemic Model
Ting-Hao Hsu, Gail S. K. Wolkowicz
We derive characteristic functions to determine the number and stability of relaxation oscillations for a class of planar systems. Applying our criterion, we give conditions under…