Finding the dimension of slow dynamics in a rhythmic system | Zendy

Shai Revzen | Zendy; John Guckenheimer | Zendy

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Finding the dimension of slow dynamics in a rhythmic system

Author(s) -

Shai Revzen,

John Guckenheimer

Publication year - 2011

Publication title -

journal of the royal society interface

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.655

H-Index - 139

eISSN - 1742-5689

pISSN - 1742-5662

DOI - 10.1098/rsif.2011.0431

Subject(s) - series (stratigraphy) , dynamical systems theory , context (archaeology) , dissipative system , computer science , nonlinear system , nonlinear dynamical systems , dynamical system (definition) , time series , statistical physics , dimension (graph theory) , periodic orbits , complex dynamics , control theory (sociology) , mathematics , physics , control (management) , artificial intelligence , mathematical analysis , machine learning , paleontology , quantum mechanics , pure mathematics , biology

Dynamical systems with asymptotically stable periodic orbits are generic models for rhythmic processes in dissipative physical systems. This paper presents a method for reconstructing the dynamics near a periodic orbit from multivariate time-series data. It is used to test theories about the control of legged locomotion, a context in which time series are short when compared with previous work in nonlinear time-series analysis. The method presented here identifies appropriate dimensions of reduced order models for the deterministic portion of the dynamics. The paper also addresses challenges inherent in identifying dynamical models with data from different individuals.

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