Novel slow–fast behaviour in an oscillator driven by a frequency-switching force
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple periodically-forced harmonic oscillator, which disagree starkly in their pred...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/400249 |
| Acceso en línea: | https://hdl.handle.net/2117/400249 https://dx.doi.org/10.1016/j.cnsns.2022.107032 |
| Access Level: | acceso abierto |
| Palabra clave: | Switching circuits Nonsmooth Filippov Slow–fast Timescale Ageing Switching Canard Circuits de commutació Àrees temàtiques de la UPC::Enginyeria elèctrica::Maquinària i aparells elèctrics::Oscil·ladors elèctrics |
| Sumario: | When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple periodically-forced harmonic oscillator, which disagree starkly in their predictions of its long time behaviour. Attempting to resolve the disagreement by ‘regularizing’ the switch not only preserves the disagreement, but shows it increases with time. One of the models corresponds to a conventional ‘Filippov’ description of a nonsmooth system, while the second exhibits a structure that irreversibly ages, developing a number of novel multi-scale behaviours that we believe have not been reported before. These include slow–fast staircases, novel mixed-mode oscillations, and a synchronized canard explosion. These features are proven to exist using asymptotic analysis, but as they involve a slow–fast time-scale separation that increases with time, they lie beyond the reach of numerical methods. |
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