Isostables for Stochastic Oscillators
| dc.contributor.author | Pérez Cervera, Alberto | |
| dc.contributor.author | Lindner, Benjamin | |
| dc.contributor.author | Thomas, Peter J. | |
| dc.date.accessioned | 2023-06-16T14:25:39Z | |
| dc.date.available | 2023-06-16T14:25:39Z | |
| dc.date.issued | 2021-12-14 | |
| dc.description.abstract | Thomas and Lindner [P. J. Thomas and B. Lindner, Phys. Rev. Lett. 113, 254101 (2014).], defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having a complex eigenvalue with a least negative real part, of the backward Kolmogorov (or stochastic Koopman) operator. We complete the phase-amplitude description of noisy oscillators by defining the stochastic isostable coordinate as the eigenfunction with the least negative nontrivial real eigenvalue. Our results suggest a framework for stochastic limit cycle dynamics that encompasses noise-induced oscillations. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/76887 | |
| dc.identifier.doi | 10.1103/PhysRevLett.127.254101 | |
| dc.identifier.issn | 0031-9007 | |
| dc.identifier.officialurl | https://doi.org/10.1103/PhysRevLett.127.254101 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/5004 | |
| dc.journal.title | Physical review letters | |
| dc.language.iso | eng | |
| dc.page.initial | 254101 | |
| dc.publisher | American Physical Society | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517 | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Isostables for Stochastic Oscillators | |
| dc.type | journal article | |
| dc.volume.number | 127 | |
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[25] We choose the Itô interpretation for its mathematical convenience. For every Stratonovich-interpreted SDE there is an equivalent Itô-interpreted SDE [26]. Thus, choosing between the Itô or the Stratonovich interpretation will not change our framework, which is based on the (uniquely defined) backward Kolmogorov operator. [26] C. W. Gardiner, Handbook of Stochastic Methods (Springerverlag, Berlin, 1985). [27] J. T. C. Schwabedal and A. Pikovsky, Phys. Rev. Lett. 110, 204102 (2013). [28] A. Cao and B. Lindner, and P. J. Thomas, SIAM J. Appl. Math. 80, 422 (2020). [29] P. J. Thomas and B. Lindner, Phys. Rev. Lett. 113, 254101 (2014). [30] For an alternative approach to phase reduction for stochastic oscillators see [27,28]. [31] P. J. Thomas and B. Lindner, Phys. Rev. E 99, 062221 (2019). [32] In the n > 2 case, we expect n − 1 stochastic amplitudes Σi corresponding to the n − 1 deterministic Floquet modes. The effective vector field would be determined by a system of n equations, e.g., ∇Q �ðxÞ · FðxÞ ¼ λ�Q �ðxÞ, ∇Σi ðxÞ · FðxÞ ¼ λi FloqΣi ðxÞ, for 1 ≤ i ≤ n − 1. If jλ1 Floqj ≪jλi Floqj for i > 1, we expect the flow generated by F will have a 2D invariant manifold Σi ¼ 0;i> 1, on which the dynamics will be well approximated by our 2D (phase, amplitude) construction. [33] See Supplemental Material at http://link.aps.org/supplemental/ 10.1103/PhysRevLett.127.254101 for the numerical procedure generating the results in this Letter. [34] T. K. Leen, R. Friel, and D. Nielsen, arXiv:1609.01194. [35] A. S. Powanwe and A. Longtin, Sci. Rep. 9, 18335 (2019). [36] N. Črnjarić-Žic, S. Maćešić, and I. Mezić, J. Nonlinear Sci. 30, 2007 (2019). [37] V. S. Afraimovich, M. I. Rabinovich, and P. Varona, Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, 1195 (2004). [38] D. Armbruster, E. Stone, and V. Kirk, Chaos 13, 71 (2003). [39] R. M. May and W. J. Leonard, SIAM J. Appl. Math. 29, 243 (1975). 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| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | de495841-c58a-47a5-b14f-3c4ba7dc9f96 | |
| relation.isAuthorOfPublication.latestForDiscovery | de495841-c58a-47a5-b14f-3c4ba7dc9f96 |
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