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arXiv · 2605.27806

Phase Plane Analysis on Time Scales for a Lotka-Volterra Competition Model

Sabrina Streipert·Gail S. K. Wolkowicz
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Abstract

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 augmented phase plane analysis that extends the traditional phase plane analysis known to be a powerful tool in the analysis of planar differential equations. In the case of a constant graininess, the method is consistent with the augmented phase portrait introduced for the discrete space. However, for non-constant graininess, this augmented phase plane is time-dependent and therefore dynamic. Despite the dynamic character, we are able to identify time-independent information that allows the conclusion of the global dynamics of the introduced Lotka--Volterra competition model on time scales. The dynamic phase plane method, albeit only introduced in the context of this particular two-species competition model, it can be extended to other planar systems on time scales, providing a novel technique to study the global dynamics of planar systems on time scales.

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Sabrina Streipert, Gail S. K. Wolkowicz. 2026-05-27. Phase Plane Analysis on Time Scales for a Lotka-Volterra Competition Model. https://arxiv.org/abs/2605.27806

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