Stochastic bifurcations of generalized Duffing–van der Pol system with fractional derivative under colored noise

The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochast...

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Published inChinese physics B Vol. 26; no. 9; pp. 62 - 69
Main Author 李伟 张美婷 赵俊锋
Format Journal Article
LanguageEnglish
Published 01.08.2017
Subjects
l系统
van
分数阶导数
广义
有色噪声
概率密度
随机分岔
Online AccessGet full text
ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/26/9/090501

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Abstract The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochastic averaging method is applied to obtain the FPK equation and the stationary probability density of the amplitude. After that, the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. Different types of stationary probability densities of the amplitude are also obtained. The study finds that the change of noise intensity, fractional order, and correlation time will lead to the stochastic bifurcation.
AbstractList The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochastic averaging method is applied to obtain the FPK equation and the stationary probability density of the amplitude. After that, the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. Different types of stationary probability densities of the amplitude are also obtained. The study finds that the change of noise intensity, fractional order, and correlation time will lead to the stochastic bifurcation.
Author 李伟 张美婷 赵俊锋
AuthorAffiliation School of Mathematics and Statistics, Xidian University, Xi＇ an 710071, China Applied Mathematics Department, School of Science, Northwestern Polytechnical University, Xi＇ an 710072, China
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Cites_doi 10.1016/j.ijnonlinmec.2011.09.012
10.7498/aps.54.2557
10.1016/j.probengmech.2010.07.008
10.1016/j.chaos.2006.05.010
10.1016/j.cnsns.2009.12.034
10.1360/132012-692
10.1007/978-3-662-12878-7
10.1016/j.jsv.2008.06.026
10.1103/PhysRevE.83.056215
10.1016/j.chaos.2005.11.066
10.7498/aps.65.210501
10.1007/s11071-015-2345-1
10.1103/PhysRevE.81.011106
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DocumentTitleAlternate Stochastic bifurcations of generalized Duffing–van der Pol system with fractional derivative under colored noise
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Notes stochastic bifurcation fractional derivative color noise stochastic averaging method
The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochastic averaging method is applied to obtain the FPK equation and the stationary probability density of the amplitude. After that, the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. Different types of stationary probability densities of the amplitude are also obtained. The study finds that the change of noise intensity, fractional order, and correlation time will lead to the stochastic bifurcation.
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References 12
Gu R C (7) 2011; 60
13
14
15
16
Wu Z Q (10) 2015; 64
Zhu W Q (17) 1992
19
Hao Y (8) 2013; 45
Xu W (11) 2016; 65
Wang X D (3) 2005; 54
Rong H W (4) 2006; 27
1
2
5
6
9
Ling F H (18) 1987
References_xml – ident: 14
  doi: 10.1016/j.ijnonlinmec.2011.09.012
– volume: 54
  start-page: 2557
  issn: 0372-736X
  year: 2005
  ident: 3
  publication-title: Acta Phys. Sin.
  doi: 10.7498/aps.54.2557
– volume: 45
  start-page: 257
  year: 2013
  ident: 8
  publication-title: Chin. J. Theor. Appl. Mech.
– ident: 13
  doi: 10.1016/j.probengmech.2010.07.008
– volume: 64
  issn: 0372-736X
  year: 2015
  ident: 10
  publication-title: Acta Phys. Sin.
– volume: 27
  start-page: 1373
  year: 2006
  ident: 4
  publication-title: Chin. J. Appl. Mech.
– year: 1992
  ident: 17
  publication-title: Random Vibration
– volume: 60
  issn: 0372-736X
  year: 2011
  ident: 7
  publication-title: Acta Phys. Sin.
– ident: 16
  doi: 10.1016/j.chaos.2006.05.010
– ident: 2
  doi: 10.1016/j.cnsns.2009.12.034
– ident: 9
  doi: 10.1360/132012-692
– ident: 1
  doi: 10.1007/978-3-662-12878-7
– ident: 12
  doi: 10.1016/j.jsv.2008.06.026
– ident: 6
  doi: 10.1103/PhysRevE.83.056215
– ident: 15
  doi: 10.1016/j.chaos.2005.11.066
– volume: 65
  start-page: 210501
  issn: 0372-736X
  year: 2016
  ident: 11
  publication-title: Acta Phys. Sin.
  doi: 10.7498/aps.65.210501
– ident: 19
  doi: 10.1007/s11071-015-2345-1
– ident: 5
  doi: 10.1103/PhysRevE.81.011106
– start-page: 4
  year: 1987
  ident: 18
  publication-title: Catastrophe Theory and its Applications
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SubjectTerms l系统
van
分数阶导数
广义
有色噪声
概率密度
随机分岔
Title Stochastic bifurcations of generalized Duffing–van der Pol system with fractional derivative under colored noise
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