Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems
Two commonly adopted expressions for the largest Lyapunov exponents of linearized stochastic systems are reviewed. Their features are discussed in light of bifurcation analysis and one expression is selected for evaluating the largest Lyapunov exponent of a linearized system. An independent method,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1996-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-1996-3410 |
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| _version_ | 1832556117140439040 |
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| author | C.W.S. To D.M. Li |
| author_facet | C.W.S. To D.M. Li |
| author_sort | C.W.S. To |
| collection | DOAJ |
| description | Two commonly adopted expressions for the largest Lyapunov exponents of linearized stochastic systems are reviewed. Their features are discussed in light of bifurcation analysis and one expression is selected for evaluating the largest Lyapunov exponent of a linearized system. An independent method, developed earlier by the authors, is also applied to determine the bifurcation points of a van der Pol oscillator under parametric random excitation. It is shown that the bifurcation points obtained by the independent technique agree qualitatively and quantitatively with those evaluated by using the largest Lyapunov exponent of the linearized oscillator. |
| format | Article |
| id | doaj-art-7ffc1349638c442da92a04d1c6db509b |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-7ffc1349638c442da92a04d1c6db509b2025-02-03T05:46:19ZengWileyShock and Vibration1070-96221875-92031996-01-013431332010.3233/SAV-1996-3410Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear SystemsC.W.S. To0D.M. Li1Department of Mechanical Engineering, University of Western Ontario, London, Ontario N6A 589, CanadaDepartment of Mechanical Engineering, University of Western Ontario, London, Ontario N6A 589, CanadaTwo commonly adopted expressions for the largest Lyapunov exponents of linearized stochastic systems are reviewed. Their features are discussed in light of bifurcation analysis and one expression is selected for evaluating the largest Lyapunov exponent of a linearized system. An independent method, developed earlier by the authors, is also applied to determine the bifurcation points of a van der Pol oscillator under parametric random excitation. It is shown that the bifurcation points obtained by the independent technique agree qualitatively and quantitatively with those evaluated by using the largest Lyapunov exponent of the linearized oscillator.http://dx.doi.org/10.3233/SAV-1996-3410 |
| spellingShingle | C.W.S. To D.M. Li Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems Shock and Vibration |
| title | Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems |
| title_full | Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems |
| title_fullStr | Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems |
| title_full_unstemmed | Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems |
| title_short | Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems |
| title_sort | largest lyapunov exponents and bifurcations of stochastic nonlinear systems |
| url | http://dx.doi.org/10.3233/SAV-1996-3410 |
| work_keys_str_mv | AT cwsto largestlyapunovexponentsandbifurcationsofstochasticnonlinearsystems AT dmli largestlyapunovexponentsandbifurcationsofstochasticnonlinearsystems |