18 citations · 52 across the 12 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
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…