4.7 Article

Synchronization and locking in oscillators with flexible periods

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CHAOS
卷 31, 期 3, 页码 -

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AMER INST PHYSICS
DOI: 10.1063/5.0021836

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资金

  1. National Science Foundation [NSF DMS 1951099]
  2. Goldwater Scholarship
  3. University of Pittsburgh Honors College (UHC) Brackenridge Fellowship
  4. UHC THINK Fellowship
  5. NASA Pennsylvania Space Grant Consortium Research Scholarship

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The study investigates the entrainment of a nonlinear oscillator by a periodic external force, and explores a two-dimensional map in which the phase and the period update according to the phase of the stimulus. The research found that there is a variety of fixed points and stability levels in different N:M-locking regions, and that the sensitivities of the phase and period to the stimulus, as well as the oscillator's preferred period, can affect the final locking pattern.
Entrainment of a nonlinear oscillator by a periodic external force is a much studied problem in nonlinear dynamics and characterized by the well-known Arnold tongues. The circle map is the simplest such system allowing for stable N: M entrainment where the oscillator produces N cycles for every M stimulus cycles. There are a number of experiments that suggest that entrainment to external stimuli can involve both a shift in the phase and an adjustment of the intrinsic period of the oscillator. Motivated by a recent model of Loehr et al. [J. Exp. Psychol.: Hum. Percept. Perform. 37, 1292 (2011)], we explore a two-dimensional map in which the phase and the period are allowed to update as a function of the phase of the stimulus. We characterize the number and stability of fixed points for different N: M-locking regions, specifically, 1:1, 1:2, 2:3, and their reciprocals, as a function of the sensitivities of the phase and period to the stimulus as well as the degree that the oscillator has a preferred period. We find that even in the limited number of locking regimes explored, there is a great deal of multi-stability of locking modes, and the basins of attraction can be complex and riddled. We also show that when the forcing period changes between a starting and final period, the rate of this change determines, in a complex way, the final locking pattern.

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