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

  • General and Applied Physics
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Abstract

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.

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Authors and Affiliations

  1. Department of Human Life Studies, Koriyama Women’s University, Koriyama, Japan

    Masamichi Ishihara

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  1. Masamichi Ishihara
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Correspondence to Masamichi Ishihara.

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Ishihara, M. Suppression of Growth by Multiplicative White Noise in a Parametric Resonant System. Braz J Phys 45, 112–119 (2015). https://doi.org/10.1007/s13538-014-0290-y

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  • DOI: https://doi.org/10.1007/s13538-014-0290-y

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