18 citations · 52 across the 12 of their papers we have counts for
12 papers
Phase Plane Analysis on Time Scales for a Lotka-Volterra Competition Model
Sabrina Streipert, Gail S. K. Wolkowicz
In this work, we formulate a two-species Lotka--Volterra competition model on time scales. To derive the global dynamics of solutions of this planar model, we introduce a dynamic a…
Adding a fecundity-survival trade-off to a discrete population model with maturation delay
Christopher J. Greyson-Gaito, Sabrina H. Streipert, Gail S. K. Wolkowicz
Although maturation delays are frequently included in population models, researchers rarely account for mortality between birth and maturity. Previous discrete population models ha…
Competition in the nutrient-driven self-cycling fermentation process
Stacey R. Smith?, Tyler Meadows, Gail S. K. Wolkowicz
Self-cycling fermentation is an automated process used for culturing microorganisms. We consider a model of distinct species competing for a single non-reproducing nutrient in…
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…
Population Growth and Competition Models with Decay and Competition Consistent Delay
Chiu-Ju Lin, Ting-Hao Hsu, Gail S. K. Wolkowicz
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density duri…
An alternative delayed population growth difference equation model
Sabrina H. Streipert, Gail S. K. Wolkowicz
We propose an alternative delayed population growth difference equation model based on a modification of the Beverton-Holt recurrence, assuming a delay only in the growth contribut…
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…
Growth on Two Limiting Essential Resources in a Self-Cycling Fermentor
Ting-Hao Hsu, Tyler Meadows, Lin Wang +1
A system of impulsive differential equations with state-dependent impulses is used to model the growth of a single population on two limiting essential resources in a self-cycling…