Order-indeterminant event-based maps for learning a beat

Document Type

Article

Publication Date

8-1-2020

Abstract

The process by which humans synchronize to a musical beat is believed to occur through error-correction where an individual's estimates of the period and phase of the beat time are iteratively adjusted to align with an external stimuli. Mathematically, error-correction can be described using a two-dimensional map where convergence to a fixed point corresponds to synchronizing to the beat. In this paper, we show how a neural system, called a beat generator, learns to adapt its oscillatory behavior through error-correction to synchronize to an external periodic signal. We construct a two-dimensional event-based map, which iteratively adjusts an internal parameter of the beat generator to speed up or slow down its oscillatory behavior to bring it into synchrony with the periodic stimulus. The map is novel in that the order of events defining the map are not a priori known. Instead, the type of error-correction adjustment made at each iterate of the map is determined by a sequence of expected events. The map possesses a rich repertoire of dynamics, including periodic solutions and chaotic orbits.

Identifier

85090180503 (Scopus)

Publication Title

Chaos

External Full Text Location

https://doi.org/10.1063/5.0013771

e-ISSN

10897682

ISSN

10541500

PubMed ID

32872826

Issue

8

Volume

30

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