Suppression of growth by multiplicative white noise in a parametric resonant system

Abstract

The author studied the growth of the amplitude in a Mathieu-like equation with multiplicative white noise. The approximate value of the exponent at the extremum on parametric resonance regions was obtained theoretically by introducing the width of time interval, and the exponents were calculated numerically by solving the stochastic differential equations by a symplectic numerical method. The Mathieu-like equation contains a parameter $\alpha$ that is determined by the intensity of noise and the strength of the coupling between the variable and the noise. The value of $\alpha$ was restricted not to be negative without loss of generality. It was shown that the exponent decreases with $\alpha$, reaches a minimum and increases after that. It was also found that the exponent as a function of $\alpha$ has only one minimum at $\alpha \ne 0$ on parametric resonance regions of $\alpha =0$. This minimum value is obtained theoretically and numerically. The existence of the minimum at $\alpha \ne 0$ indicates the suppression of the growth by multiplicative white noise.

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References in corpus (9)

• Reheating in the Presence of Noise
• System size stochastic resonance in a model for opinion formation
• Anomalous diffusion in nonlinear oscillators with multiplicative noise
• Inflationary Reheating in Grand Unified Theories
• Noise-induced reentrant transition of the stochastic Duffing oscillator
• Effects of parametric noise on a nonlinear oscillator
• Effects of white noise on parametric resonance in $\lambda {\varphi }^4$ theory
• Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point
• Amplification induced by white noise