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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.27806 |
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| _version_ | 1866911723386044416 |
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| author | Streipert, Sabrina Wolkowicz, Gail S. K. |
| author_facet | Streipert, Sabrina Wolkowicz, Gail S. K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27806 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase Plane Analysis on Time Scales for a Lotka-Volterra Competition Model Streipert, Sabrina Wolkowicz, Gail S. K. Dynamical Systems 34N05 G.2.3 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. |
| title | Phase Plane Analysis on Time Scales for a Lotka-Volterra Competition Model |
| topic | Dynamical Systems 34N05 G.2.3 |
| url | https://arxiv.org/abs/2605.27806 |