Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theoretical analysis for critical fluctuations of relaxation trajectory
  near a saddle-node bifurcation   A Langevin equation whose deterministic part undergoes a saddle-node
bifurcation is investigated theoretically. It is found that statistical
properties of relaxation trajectories in this system exhibit divergent
behaviors near a saddle-node bifurcation point in the weak-noise limit, while
the final value of the deterministic solution changes discontinuously at the
point. A systematic formulation for analyzing a path probability measure is
constructed on the basis of a singular perturbation method. In this
formulation, the critical nature turns out to originate from the neutrality of
exiting time from a saddle-point. The theoretical calculation explains results
of numerical simulations.

18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys