Predicting non-stationary and stochastic activation of saddle-node bifurcation

Jinki Kim, R. L. Harne, K. W. Wang

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


Accurately predicting the onset of large behavioral deviations associated with saddle-node bifurcations is imperative in a broad range of sciences and for a wide variety of purposes, including ecological assessment, signal amplification, and adaptive material/structure applications such as structural health monitoring and piezoelectric energy harvesting. In many such practices, noise and non-stationarity are unavoidable and ever-present influences. As a result, it is critical to simultaneously account for these two factors towards the estimation of parameters that may induce sudden bifurcations. Here, a new analytical formulation is presented to accurately determine the probable time at which a system undergoes an escape event as governing parameters are swept towards a saddle-node bifurcation point in the presence of noise. The double-well Duffing oscillator serves as the archetype system of interest since it possesses a dynamic saddle-node bifurcation. Using this archetype example, the stochastic normal form of the saddle-node bifurcation is derived from which expressions of the escape statistics are formulated. Non-stationarity is accounted for using a time dependent bifurcation parameter in the stochastic normal form. Then, the mean escape time is approximated from the probability density function to yield a straightforward means to estimate the point of bifurcation. Experiments conducted using a double-well Duffing analog circuit verify that the analytical approximations provide faithful estimation of the critical parameters that lead to the non-stationary and noise-activated saddle-node bifurcation.

Original languageEnglish (US)
Title of host publicationModeling, Simulation and Control; Bio-Inspired Smart Materials and Systems; Energy Harvesting
PublisherAmerican Society of Mechanical Engineers
ISBN (Electronic)9780791850497
StatePublished - 2016
EventASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2016 - Stowe, United States
Duration: Sep 28 2016Sep 30 2016

Publication series

NameASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2016


OtherASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2016
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Building and Construction
  • Civil and Structural Engineering
  • Control and Systems Engineering
  • Mechanics of Materials


Dive into the research topics of 'Predicting non-stationary and stochastic activation of saddle-node bifurcation'. Together they form a unique fingerprint.

Cite this