| Autor: |
Carvalho, Tiago, Novaes, Douglas D., Tonon, Durval J. |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Journal of Nonlinear Science 34, 70 (2024) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00332-024-10052-4 |
| Popis: |
We consider piecewise smooth vector fields $Z=(Z_+, Z_-)$ defined in $\mathbb{R}^n$ where both vector fields are tangent to the switching manifold $\Sigma$ along a submanifold $M\subset \Sigma$. We shall see that, under suitable assumptions, Filippov convention gives rise to a unique sliding mode on $M$, governed by what we call the {\it tangential sliding vector field}. Here, we will provide the necessary and sufficient conditions for characterizing such a vector field. Additionally, we prove that the tangential sliding vector field is conjugated to the reduced dynamics of a singular perturbation problem arising from the Sotomayor-Teixeira regularization of $Z$ around $M$. Finally, we analyze several examples where tangential sliding vector fields can be observed, including a model for intermittent treatment of HIV. |
| Databáze: |
arXiv |
| Externí odkaz: |
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