Related Experiment Video
Updated: Jun 8, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation
1Department of Pure and Applied Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan. iwata@jiro.c.u-tokyo.ac.jp
Abstract:
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.
Related Concept Videos
Limits with Oscillating Discontinuities
Stability
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Node Analysis for AC Circuits
To unravel the complexities of this system, nodal analysis is employed, a powerful technique founded on Kirchhoff's current law (KCL), which remains valid for phasors. AC circuits can effectively be...
Plotting and Calibrating the Root Locus
The maximum gain occurs at the breakaway points between open-loop poles on the real axis, while the minimum gain is observed...
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Alternating Series and Absolute Convergence
