Related Experiment Video
Updated: May 23, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Generalized Lyapunov exponents of the random harmonic oscillator: cumulant expansion approach
Raúl O Vallejos1, Celia Anteneodo
1Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil. vallejos@cbpf.br
Abstract:
The cumulant expansion is used to estimate generalized Lyapunov exponents of the random-frequency harmonic oscillator. Three stochastic processes are considered: Gaussian white noise, Ornstein-Uhlenbeck, and Poisson shot noise. In some cases, nontrivial numerical difficulties arise. These are mostly solved by implementing an appropriate importance-sampling Monte Carlo scheme. We analyze the relation between random-frequency oscillators and many-particle systems with pairwise interactions like the Lennard-Jones gas.
Related Concept Videos
Exponential Fourier series
Euler's identity...
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Exponential and Sinusoidal Signals
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Types of Responses of Series RLC Circuits
