Homoclinic and Heteroclinic Trajectories of Differential Equations with Piecewise Constant Arguments of Generalized Type
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913731068297216 |
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| author | Fen, Mehmet Onur Fen, Fatma Tokmak |
| author_facet | Fen, Mehmet Onur Fen, Fatma Tokmak |
| contents | Quasilinear systems with piecewise constant arguments of generalized type are under investigation from the asymptotic point of view. The systems have discontinuous right-hand sides which are identified via a discrete-time map. It is rigorously proved that homoclinic and heteroclinic solutions are generated, and they are taken into account in the functional sense. The Banach fixed point theorem is used for the verification. The hyperbolic set of solutions is also discussed, and an example supporting the theoretical findings is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homoclinic and Heteroclinic Trajectories of Differential Equations with Piecewise Constant Arguments of Generalized Type Fen, Mehmet Onur Fen, Fatma Tokmak Dynamical Systems 34K16, 34K34, 37C29 Quasilinear systems with piecewise constant arguments of generalized type are under investigation from the asymptotic point of view. The systems have discontinuous right-hand sides which are identified via a discrete-time map. It is rigorously proved that homoclinic and heteroclinic solutions are generated, and they are taken into account in the functional sense. The Banach fixed point theorem is used for the verification. The hyperbolic set of solutions is also discussed, and an example supporting the theoretical findings is provided. |
| title | Homoclinic and Heteroclinic Trajectories of Differential Equations with Piecewise Constant Arguments of Generalized Type |
| topic | Dynamical Systems 34K16, 34K34, 37C29 |
| url | https://arxiv.org/abs/2503.08885 |