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Synchronization and locking in oscillators with flexible periods

Savinov, Mariya Alisa (2020) Synchronization and locking in oscillators with flexible periods. Undergraduate Thesis, University of Pittsburgh. (Unpublished)

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Abstract

Upon interaction with a stimulus sequence, an oscillator may assume the stimulus' period via a process called entrainment. Standard models of entrainment assume that the oscillator has a fixed natural period and, thus, a limited range of periods to which it can entrain. However, experiments have shown that some oscillating systems have flexible periods; that is, the period of the oscillator can be changed due to external stimuli, and this period persists when the stimulus is discontinued. Studying this type of coordination, Loehr et al. (2011) showed that the synchronization of pianists with a metronome can be described by a nonlinear oscillator model that is quantitatively described using a circle map of phase and period with sinusoidal coupling terms. Here we introduce two variants, termed the multiplicative and additive forced oscillator models, so-called based on their period descriptions. Unlike the Loehr et al. model, these models include a preferred period, as most biological oscillating systems will oscillate at a fixed natural period when not experiencing driving or damping forces. This study focuses on the stability of points of N:M locking, a complex type of entrainment in which the phase of a model rotates N times in response to M stimuli. Locking types investigated here are 1:1, 1:2, 2:3, along with their reciprocals. We identify numerous parameter regimes of multi-stability, and how such regions evolve with changes in preferred period elasticity. Such multi-stability is not generally possible without a malleable period. The basins of attraction of the various types of N:M locking are investigated, with observations of fractal behavior and remarks on how the domains of attraction depend on coupling and elasticity parameters. Finally, we compare and contrast the multiplicative and additive models with other models of synchronization and beat-keeping.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Savinov, Mariya Alisamasha@pitt.edumasha
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairErmentrout, G. Bardbard@pitt.edu
Committee MemberSwigon, Davidswigon@pitt.edu
Committee MemberRubin, Jonathanjonrubin@pitt.edu
Committee MemberNeilan, Rachaelrachael.neilan@gmail.com
Date: 1 May 2020
Date Type: Publication
Defense Date: 23 March 2020
Approval Date: 1 May 2020
Submission Date: 25 March 2020
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 61
Institution: University of Pittsburgh
Schools and Programs: University Honors College
Degree: BPhil - Bachelor of Philosophy
Thesis Type: Undergraduate Thesis
Refereed: Yes
Uncontrolled Keywords: entrainment, dynamical system, circle map
Date Deposited: 01 May 2020 19:13
Last Modified: 01 May 2020 19:13
URI: http://d-scholarship.pitt.edu/id/eprint/38390

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