Study of noise-induced transitions in the Lorenz system using the minimum action method. (English) Zbl 1202.34104

Zhou, Xiang; E, Weinan

Commun. Math. Sci. 8, No. 2, 341-355 (2010).

The authors study the behaviour of noise-induced transitions in non-gradient systems when complex invariant sets emerge. Specific attention is paid to the Lorenz system, before the homoclininc explosion bifurcation and when the chaotic invariant set emerges. Further, based on the Freidlin-Wentzell theory, they use the minimum action method to identify the optimal transition path.

Reviewer: Andrew Dale (Durban)

MSC:

34F05	Ordinary differential equations and systems with randomness
34D10	Perturbations of ordinary differential equations
34C28	Complex behavior and chaotic systems of ordinary differential equations
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

noise-induced transitions; Lorenz system; limit cycle; transition set; minimum action path