Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2605.27806 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
Sommario:
- 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.