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Describing dynamics of driven multistable oscillators with phase transfer curves
Evgeny Grines1, Grigory Osipov1, Arkady Pikovsky1
1Department of Control Theory and Dynamics of Systems, Lobachevsky State University of Nizhny Novgorod, 23, Prospekt Gagarina, Nizhny Novgorod 603950, Russia.
Chaos (Woodbury, N.Y.)
|November 3, 2018
Summary
Researchers introduce phase transfer curves to analyze transitions between oscillating modes in multistable oscillators. These curves help create simplified models for periodically perturbed systems, offering accurate dynamics approximations.
Area of Science:
- Nonlinear dynamics
- Oscillatory systems analysis
Background:
- Phase response curves are crucial for understanding self-sustained oscillations and phase shifts from perturbations.
- Multistable oscillators exhibit multiple stable limit cycles, allowing for transitions between oscillating modes.
Purpose of the Study:
- To define and utilize phase transfer curves for analyzing mode transitions in multistable oscillators.
- To develop one-dimensional maps for characterizing periodically perturbed multistable oscillators.
Main Methods:
- Defining phase transfer curves to quantify phase shifts during transitions between oscillating modes.
- Constructing one-dimensional maps based on phase transfer curves for periodically kicked multistable oscillators.
Main Results:
- Phase transfer curves effectively describe phase shifts during transitions between oscillating modes.
- One-dimensional maps derived from these curves provide accurate approximations of the full dynamics for large forcing periods.
Conclusions:
- Phase transfer curves offer a novel method for characterizing complex dynamics in multistable oscillators.
- The developed one-dimensional maps serve as valuable, simplified models for periodically perturbed multistable systems.
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