| Autor: |
Karim Yadi |
| Rok vydání: |
2014 |
| Předmět: |
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| Zdroj: |
Journal of Mathematical Analysis and Applications. 413:976-998 |
| ISSN: |
0022-247X |
| DOI: |
10.1016/j.jmaa.2013.12.044 |
| Popis: |
Pontryagin–Rodyginʼs Theorem for slow and fast systems describes the slow drift during the rolling up of the trajectories around the cycles of the fast dynamics. This drift is approximated by the averaging on the cycles. The calculation of this average is generally a difficult task since it requires the knowledge of the closed orbits and their periods. We present two paradigms of three time scale systems where we can overcome this limitation. It is the case of systems the fast dynamics of which have cycles with relaxation presenting or not a canard phenomenon. We can not apply Pontryagin–Rodyginʼs Theorem to these systems because their fast equation is itself singularly perturbed. We also investigate the extension of the results to unbounded time intervals. The results are stated classically and proved within the framework of nonstandard analysis. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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