Contribution to Book
Predicting Non-Stationary and Stochastic Activation of Saddle-Node Bifurcation
Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems
(2016)
Abstract
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 microscale mass sensing. 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 toward 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 toward 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. The stochastic normal form of the saddle-node bifurcation is derived from the governing equation of this oscillator to formulate the probability distribution of escape events. 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 (PDF) to yield a straightforward means to estimate the point of bifurcation. Experiments conducted using a double-well Duffing analog circuit verifies that the analytical approximations provide faithful estimation of the critical parameters that lead to the non-stationary and noise-activated saddle-node bifurcation.
Keywords
- Predicting,
- Non-stationary,
- Stochastic activation,
- Saddle-node bifurcation
Disciplines
Publication Date
September 28, 2016
Publisher
American Society of Mechanical Engineers
ISBN
978-0-7918-5049-7
DOI
10.1115/SMASIS2016-9051
Citation Information
Jinki Kim, Ryan L. Harne and Kon-Well Wang. "Predicting Non-Stationary and Stochastic Activation of Saddle-Node Bifurcation" Stowe, VTProceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems (2016) Available at: http://works.bepress.com/jinki-kim/7/