Correlation times in stochastic equations with delayed feedback and multiplicative noise
Loading...
External sources
External sources
Date
Advisor
Coadvisor
Graduate program
Undergraduate course
Journal Title
Journal ISSN
Volume Title
Publisher
Amer Physical Soc
American Physical Society (APS)
American Physical Society (APS)
Type
Article
Access right
Acesso aberto
External sources
External sources
Abstract
We obtain the characteristic correlation time associated with a model stochastic differential equation that includes the normal form of a pitchfork bifurcation and delayed feedback. In particular, the validity of the common assumption of statistical independence between the state at time t and that at t - tau, where t is the delay time, is examined. We find that the correlation time diverges at the model's bifurcation line, thus signaling a sharp bifurcation threshold, and the failure of statistical independence near threshold. We determine the correlation time both by numerical integration of the governing equation, and analytically in the limit of small tau. The correlation time T diverges as T similar to a(-1), where a is the control parameter so that a = 0 is the bifurcation threshold. The small-tau expansion correctly predicts the location of the bifurcation threshold, but there are systematic deviations in the magnitude of the correlation time.
Description
Keywords
Language
English
Citation
Physical Review E. College Pk: Amer Physical Soc, v. 83, n. 1, p. 6, 2011.
