Information-theoretic characterization of bifurcations in nonlinear dynamical systems with noise

Navendu S. Patil, Joseph Paul Cusumano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Detecting bifurcations in noisy and/or high-dimensional physical systems is an important problem in nonlinear dynamics. Near bifurcations, the dynamics of even a high dimensional system is typically dominated by its behavior on a low dimensional manifold. Since the system is sensitive to perturbations near bifurcations, they can be detected by looking at the apparent deterministic structure generated by the interaction between the noise and low-dimensional dynamics. We use minimal hidden Markov models built from the noisy time series to quantify this deterministic structure at the period-doubling bifurcations in the two-well forced Duffing oscillator perturbed by noise. The apparent randomness in the system is characterized using the entropy rate of the discrete stochastic process generated by partitioning time series data. We show that as the bifurcation parameter is varied, sharp changes in the statistical complexity and the entropy rate can be used to locate incipient bifurcations.

Original languageEnglish (US)
Title of host publication9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers
ISBN (Print)9780791855973
DOIs
StatePublished - Jan 1 2013
EventASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 - Portland, OR, United States
Duration: Aug 4 2013Aug 7 2013

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume7 B

Other

OtherASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013
CountryUnited States
CityPortland, OR
Period8/4/138/7/13

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All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Cite this

Patil, N. S., & Cusumano, J. P. (2013). Information-theoretic characterization of bifurcations in nonlinear dynamical systems with noise. In 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control [V07BT10A035] (Proceedings of the ASME Design Engineering Technical Conference; Vol. 7 B). American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2013-13519