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

Fingerprint

Nonlinear dynamical systems
Nonlinear Dynamical Systems
Bifurcation
Time series
Entropy
Hidden Markov models
Random processes
High-dimensional
Duffing Oscillator
Period-doubling Bifurcation
Time Series Data
Randomness
Nonlinear Dynamics
Markov Model
Stochastic Processes
Partitioning
Quantify
Perturbation
Interaction

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
Patil, Navendu S. ; Cusumano, Joseph Paul. / Information-theoretic characterization of bifurcations in nonlinear dynamical systems with noise. 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. American Society of Mechanical Engineers, 2013. (Proceedings of the ASME Design Engineering Technical Conference).
@inproceedings{fd55f812fc3c4e1dbcd6a6f3f99b5a7e,
title = "Information-theoretic characterization of bifurcations in nonlinear dynamical systems with noise",
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.",
author = "Patil, {Navendu S.} and Cusumano, {Joseph Paul}",
year = "2013",
month = "1",
day = "1",
doi = "10.1115/DETC2013-13519",
language = "English (US)",
isbn = "9780791855973",
series = "Proceedings of the ASME Design Engineering Technical Conference",
publisher = "American Society of Mechanical Engineers",
booktitle = "9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control",

}

Patil, NS & Cusumano, JP 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, ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013, Portland, OR, United States, 8/4/13. https://doi.org/10.1115/DETC2013-13519

Information-theoretic characterization of bifurcations in nonlinear dynamical systems with noise. / Patil, Navendu S.; Cusumano, Joseph Paul.

9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. American Society of Mechanical Engineers, 2013. V07BT10A035 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 7 B).

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

TY - GEN

T1 - Information-theoretic characterization of bifurcations in nonlinear dynamical systems with noise

AU - Patil, Navendu S.

AU - Cusumano, Joseph Paul

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84896926191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896926191&partnerID=8YFLogxK

U2 - 10.1115/DETC2013-13519

DO - 10.1115/DETC2013-13519

M3 - Conference contribution

AN - SCOPUS:84896926191

SN - 9780791855973

T3 - Proceedings of the ASME Design Engineering Technical Conference

BT - 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

PB - American Society of Mechanical Engineers

ER -

Patil NS, Cusumano JP. Information-theoretic characterization of bifurcations in nonlinear dynamical systems with noise. In 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. American Society of Mechanical Engineers. 2013. V07BT10A035. (Proceedings of the ASME Design Engineering Technical Conference). https://doi.org/10.1115/DETC2013-13519