Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explore Stochastic Instabilities of Periodic Points by Transition Path
  Theory   We consider the noise-induced transitions in the randomly perturbed discrete
logistic map from a linearly stable periodic orbit consisting of T periodic
points. The traditional large deviation theory and asymptotic analysis for
small noise limit as well as the derived quasi-potential can not distinguish
the quantitative difference in noise-induced stochastic instabilities of these
T periodic points. We generalize the transition path theory to the
discrete-time continuous-space stochastic process to attack this problem. As a
first criterion of quantifying the relative instability among T periodic
points, we compare the distribution of the last passage locations in the
transitions from the whole periodic orbit to a prescribed set far away. This
distribution is related to the contributions to the transition rate from each
periodic points. The second criterion is based on the competency of the
transition paths associated with each periodic point. Both criteria utilise the
reactive probability current in the transition path theory. Our numerical
results for the logistic map reveal the transition mechanism of escaping from
the stable periodic orbit and identify which peri- odic point is more prone to
lose stability so as to make successful transitions under random perturbations.

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The categories of this paper are: math
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: physics
24
The categories of this paper are: dg-ga