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Mathematics > Dynamical Systems

Title: Stochastic basins of attraction and generalized committor functions

Abstract: We generalize the concept of basin of attraction of a stable state in order to facilitate the analysis of dynamical systems with noise and to assess stability properties of metastable states and long transients. To this end we examine the notions of mean sojourn times and absorption probabilities for Markov chains and study their convergence to the basin of attraction in the limiting cases. Since any dynamical system described by a transfer operator on a compact domain can be approximated by a Markov chain our approach is applicable to a large variety of problems.
Subjects: Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)
Cite as: arXiv:1803.06372 [math.DS]
  (or arXiv:1803.06372v1 [math.DS] for this version)

Submission history

From: Michael Lindner [view email]
[v1] Fri, 16 Mar 2018 19:03:05 GMT (370kb,D)