Journal
PHYSICAL REVIEW E
Volume 82, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.82.011127
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Funding
- Ministry of Education, Science, Sports and Culture of Japan [19540394, 21015005]
- Hayashi Memorial Foundation
- Grants-in-Aid for Scientific Research [21015005, 19540394] Funding Source: KAKEN
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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.
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