P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White Noise
This work aims to address the P-bifurcation of a stochastic nonlinear system with fractional damping driven by Gaussian white noise. Based on a stochastic averaging method, a fractional damping stochastic nonlinear equation has been studied. Furthermore, the expressions of drift and diffusion coeffi...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/5/408 |
| _version_ | 1797600016986013696 |
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| author | Yujie Tang Yun Peng Guitian He Wenjie Liang Weiting Zhang |
| author_facet | Yujie Tang Yun Peng Guitian He Wenjie Liang Weiting Zhang |
| author_sort | Yujie Tang |
| collection | DOAJ |
| description | This work aims to address the P-bifurcation of a stochastic nonlinear system with fractional damping driven by Gaussian white noise. Based on a stochastic averaging method, a fractional damping stochastic nonlinear equation has been studied. Furthermore, the expressions of drift and diffusion coefficients of the Fokker–Planck equation (FPKE) have been obtained. The probability density function (PDF), the steady solution of FPKE, has also been derived. Then, PDFs of two fractional damping Morse oscillators have been obtained. One can note that the analytical results coincide with the results of numerical simulation. Importantly, stochastic P-bifurcation of a fractional damping stochastic nonlinear Morse oscillator has been further addressed and analyzed. |
| first_indexed | 2024-03-11T03:42:31Z |
| format | Article |
| id | doaj.art-477a903f1dac4eeab6d2c1b431649123 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T03:42:31Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-477a903f1dac4eeab6d2c1b4316491232023-11-18T01:26:42ZengMDPI AGFractal and Fractional2504-31102023-05-017540810.3390/fractalfract7050408P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White NoiseYujie Tang0Yun Peng1Guitian He2Wenjie Liang3Weiting Zhang4College of Mathematics and Physics, Center for Applied Mathematics of Guangxi Minzu University, Nanning 530006, ChinaCollege of Mathematics and Physics, Center for Applied Mathematics of Guangxi Minzu University, Nanning 530006, ChinaCollege of Mathematics and Physics, Center for Applied Mathematics of Guangxi Minzu University, Nanning 530006, ChinaCollege of Mathematics and Physics, Center for Applied Mathematics of Guangxi Minzu University, Nanning 530006, ChinaCollege of Mathematics and Physics, Center for Applied Mathematics of Guangxi Minzu University, Nanning 530006, ChinaThis work aims to address the P-bifurcation of a stochastic nonlinear system with fractional damping driven by Gaussian white noise. Based on a stochastic averaging method, a fractional damping stochastic nonlinear equation has been studied. Furthermore, the expressions of drift and diffusion coefficients of the Fokker–Planck equation (FPKE) have been obtained. The probability density function (PDF), the steady solution of FPKE, has also been derived. Then, PDFs of two fractional damping Morse oscillators have been obtained. One can note that the analytical results coincide with the results of numerical simulation. Importantly, stochastic P-bifurcation of a fractional damping stochastic nonlinear Morse oscillator has been further addressed and analyzed.https://www.mdpi.com/2504-3110/7/5/408stochastic averaging procedurefractional derivativeP-bifurcationMorse oscillatorGaussian white noise |
| spellingShingle | Yujie Tang Yun Peng Guitian He Wenjie Liang Weiting Zhang P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White Noise Fractal and Fractional stochastic averaging procedure fractional derivative P-bifurcation Morse oscillator Gaussian white noise |
| title | P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White Noise |
| title_full | P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White Noise |
| title_fullStr | P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White Noise |
| title_full_unstemmed | P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White Noise |
| title_short | P-Bifurcation Analysis for a Fractional Damping Stochastic Nonlinear Equation with Gaussian White Noise |
| title_sort | p bifurcation analysis for a fractional damping stochastic nonlinear equation with gaussian white noise |
| topic | stochastic averaging procedure fractional derivative P-bifurcation Morse oscillator Gaussian white noise |
| url | https://www.mdpi.com/2504-3110/7/5/408 |
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