Papers › An augmented phase plane approach for discrete planar maps: Introducing next-iterate operators
An augmented phase plane approach for discrete planar maps: Introducing next-iterate operators
Sabrina H. Streipert, Gail S. K. Wolkowicz
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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 phase portraits that include the nullclines and the direction field, by including the signs of the root-operators associated with their nullclines, thus producing an augmented phase portrait, is described. The sign of a next-iterate operator associated with a nullcline determines whether a point is mapped above or below the corresponding nullcline and can, for example, identify positively invariant regions. Using a Lotka-Volterra type competition model, we demonstrate how to construct the augmented phase portrait. We show that the augmented phase portrait provides an elementary, alternative approach for determining the complete global dynamics of this model. We further explore the limitations and potential of the augmented phase portrait by considering a Ricker competition model, a model involving mutualism, and a predator-prey model.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections