We extend the recently developed generalized Floquet theory [Phys. Rev. Lett. 110, 170602 (2013)] to systems with innite memory, i.e., a dependence on the whole previous history. In particular, we show that a lower asymptotic bound exists for the Floquet exponents associated to such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian particle, and a circuit resonator with an ideal transmission line. All these examples show the usefulness of this new approach to the study of dynamical systems with memory, which are ubiquitous in science and technology.

Application of Floquet theory to dynamical systems with memory / Traversa, Fabio L.; Di Ventra, Massimiliano; Cappelluti, Federica; Bonani, Fabrizio. - In: CHAOS. - ISSN 1054-1500. - ELETTRONICO. - 30:12(2020), p. 123102. [10.1063/5.0016058]

Application of Floquet theory to dynamical systems with memory

Traversa, Fabio L.;Cappelluti, Federica;Bonani, Fabrizio
2020

Abstract

We extend the recently developed generalized Floquet theory [Phys. Rev. Lett. 110, 170602 (2013)] to systems with innite memory, i.e., a dependence on the whole previous history. In particular, we show that a lower asymptotic bound exists for the Floquet exponents associated to such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian particle, and a circuit resonator with an ideal transmission line. All these examples show the usefulness of this new approach to the study of dynamical systems with memory, which are ubiquitous in science and technology.
File in questo prodotto:
File Dimensione Formato  
CHA20-AR-00781.pdf

accesso aperto

Descrizione: Articolo principale post referee
Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 1.22 MB
Formato Adobe PDF
1.22 MB Adobe PDF Visualizza/Apri
Chaos 20.pdf

Open Access dal 02/12/2021

Descrizione: Articolo principale
Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 1.6 MB
Formato Adobe PDF
1.6 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2854366