Small noise limit for diffusions near heteroclinic networks

Abstract

This is a nontechnical exposition of the theory on vanishing noise limit for random perturbations of dynamical systems admitting heteroclinic networks developed by the author [Y. Bakhtin, Noisy heteroclinic networks, Probability Theory Rel. Fields (2010) DOI: 10.1007/s00440-010-0264-0]. We avoid details on stochastic calculus and stress the main ideas.

Keywords:

• heteroclinic networks
• small noise
• random perturbation
• exit distribution

AMS Subject Classifications::

• 60J60
• 34E10
• 60F17

Acknowledgments

The author is grateful to NSF for support via a CAREER grant DMS-0742424.