Anomalous diffusion in nonlinear oscillators with multiplicative noise

Abstract

The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy, root-mean-square position and velocity, grow algebraically with time. The scaling exponents and associated generalized diffusion constants are calculated when the oscillator's potential energy grows as a power of its position. Correlated noise yields anomalous diffusion exponents equal to half the value found for white noise.

22 pages, 20 figures, extended version of a paper to be published in Physical Review E

References in corpus (4)

• Brownian motors: noisy transport far from equilibrium
• Recent results on multiplicative noise
• Adiabatic reduction near a bifurcation in stochastically modulated systems
• Anderson localization as a parametric instability of the linear kicked oscillator

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