Suppression of Growth by Multiplicative White Noise in a Parametric Resonant System

• Published in: Brazilian journal of physics Vol. 45; no. 1; pp. 112 - 119
• Main Author: Ishihara, Masamichi
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.02.2015
• Subjects: General and Applied Physics; Physics; Physics and Astronomy; Multiplicative White Noise; Suppression of growth; Exponent; Parametric Resonance
• ISSN: 0103-9733; 1678-4448
• DOI: 10.1007/s13538-014-0290-y

The growth of the amplitude in a Mathieu-like equation with multiplicative white noise is studied. To obtain an approximate analytical expression for the exponent at the extremum on parametric resonance regions, a time-interval width is introduced. To determine the exponents numerically, the stochastic differential equations are solved by a symplectic numerical method. The Mathieu-like equation contains a parameter α determined by the intensity of noise and the strength of the coupling between the variable and noise; without loss of generality, only non-negative α can be considered. The exponent is shown to decrease with α , reach a minimum and increase after that. The minimum exponent is obtained analytically and numerically. As a function of α , the minimum at α ≠0, occurs on the parametric resonance regions of α =0. This minimum indicates suppression of growth by multiplicative white noise.