This dissertation considers a periodically-forced 1-D Langevin equation that possesses two stable periodic solutions in the absence of noise. We aim at answering the question: is there a most likely noise-induced transition path between these periodic solutions that allows one to identify a preferred phase of the forcing when the transition (or tipping event) occurs? The slow forcing regime, where the forcing period is long compared to the adiabatic relaxation time, has been well studied; the work presented in this dissertation instead explores the case when the relaxation time and the forcing period are comparable. We compute optimal paths using the path integral method incorporating the Onsager-Machlup functional and validate results with Monte Carlo simulations. Results for the preferred tipping phase are compared with the deterministic aspects of the problem. We identify parameter regimes where nullclines, associated with the deterministic problem in a 2-D extended phase space, form passageways through which the optimal paths transit. As the nullclines are independent of the relaxation time and the noise strength, this leads to a robust deterministic predictor of preferred tipping phase in a regime where forcing is neither too fast, nor too slow.

Creator

• Chen, Yuxin

DOI

• https://doi.org/10.21985/n2-jzch-t478

Subject

• Applied mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:14754
• etdadmin_upload_677031

Date created

• 2019-01-01

Resource type

• Dissertation

Rights statement

• In Copyright