| Full text | |
| Author(s): |
Gaudreault, Mathieu
;
Berbert, Juliana Militao
;
Vinals, Jorge
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Physical Review E; v. 83, n. 1, p. 6-pg., 2011-01-11. |
| 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. (AU) | |
| FAPESP's process: | 09/11567-6 - Spatial problems in population dynamics |
| Grantee: | Juliana Militão da Silva Berbert |
| Support Opportunities: | Scholarships in Brazil - Doctorate |