Variational superposed Gaussian approximation for time-dependent solutions of Langevin equations
We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaot...
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| Published in | arXiv.org |
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| Main Author | |
| Format | Paper Journal Article |
| Language | English |
| Published |
Ithaca
Cornell University Library, arXiv.org
01.04.2015
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| ISSN | 2331-8422 |
| DOI | 10.48550/arxiv.1411.3076 |
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| Abstract | We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises. |
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| AbstractList | We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises. Physical Review E, 91, 042912 (2015) We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises. |
| Author | Hasegawa, Yoshihiko |
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| BackLink | https://doi.org/10.48550/arXiv.1411.3076$$DView paper in arXiv https://doi.org/10.1103/PhysRevE.91.042912$$DView published paper (Access to full text may be restricted) |
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| Copyright | 2015. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
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| DOI | 10.48550/arxiv.1411.3076 |
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| Snippet | We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining... Physical Review E, 91, 042912 (2015) We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to... |
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| SubjectTerms | Approximation Computer simulation Mathematical analysis Noise intensity Physics - Statistical Mechanics Probability density functions Stochastic resonance Time dependence Variations |
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