Phase and frequency linear response theory for hyperbolic chaotic oscillators
- We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture, stating the existence of a perturbed trajectory shadowing every unperturbed trajectory on the system attractor for any small enough perturbation of arbitrary duration and a corresponding unique time isomorphism, which we identify as phase such that phase shifts between the unperturbed trajectory and its perturbed shadow are well defined. The phase sensitivity function is the solution of an adjoint linear equation and can be used to estimate the average change of phase velocity to small time dependent or independent perturbations. These changes in frequency are experimentally accessible, giving a convenient way to define and measure phase response curves for chaotic oscillators. The shadowing trajectory and the phase can be constructed explicitly in the tangent space of an unperturbed trajectory usingWe formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture, stating the existence of a perturbed trajectory shadowing every unperturbed trajectory on the system attractor for any small enough perturbation of arbitrary duration and a corresponding unique time isomorphism, which we identify as phase such that phase shifts between the unperturbed trajectory and its perturbed shadow are well defined. The phase sensitivity function is the solution of an adjoint linear equation and can be used to estimate the average change of phase velocity to small time dependent or independent perturbations. These changes in frequency are experimentally accessible, giving a convenient way to define and measure phase response curves for chaotic oscillators. The shadowing trajectory and the phase can be constructed explicitly in the tangent space of an unperturbed trajectory using co-variant Lyapunov vectors. It can also be used to identify the limits of the regime of linear response.…
Author details: | Ralf TönjesORCiDGND, Hiroshi KoriORCiD |
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DOI: | https://doi.org/10.1063/5.0064519 |
ISSN: | 1054-1500 |
ISSN: | 1089-7682 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/35489838 |
Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
Publisher: | AIP Publishing |
Place of publishing: | Melville |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/04/18 |
Publication year: | 2022 |
Release date: | 2023/12/07 |
Volume: | 32 |
Issue: | 4 |
Article number: | 043124 |
Number of pages: | 13 |
Funding institution: | MEXT KAKENHI [15H05876]; JSPS KAKENHI [18K11464] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |