Resonance and limit cycle in a noise driven Lorenz model

TL;DR

This paper investigates how external noise influences the Lorenz model, revealing a diverging time scale and resonance phenomena near critical bifurcations, and explains noise-induced stabilization of limit cycles.

Contribution

It provides a theoretical understanding of noise effects on the Lorenz model, including resonance and stabilization mechanisms near bifurcations.

Findings

Diverging time scale near convection onset

Resonance near Hopf bifurcation

Noise-induced stabilization of limit cycles

Abstract

The effect of an external noise on the Lorenz model is investigated near the onset of convection and near the Hopf bifurcation. We show the existence of a diverging time scale near the onset of convection and a resonance near the Hopf bifurcation. Our calculation provides an understanding of the noise induced stabilization of the limit cycle that had been observed numerically.