Lyapunov Exponents and Moment Lyapunov Exponents of a Two-Dimensional Near-Nilpotent SystemSource: Journal of Applied Mechanics:;2001:;volume( 068 ):;issue: 003::page 453Author:W.-C. Xie
DOI: 10.1115/1.1364491Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The Lyapunov exponents and moment Lyapunov exponents of a near-nilpotent system under stochastic parametric excitation are studied. The system considered is the linearized system of a two-dimensional nonlinear system exhibiting a pitchfork bifurcation. The effect of stochastic perturbation in the vicinity of static pitchfork bifurcation is investigated. Approximate analytical results of Lyapunov exponent are obtained. The eigenvalue problem for the moment Lyapunov exponent is converted to a two-point boundary value problem, which is solved numerically by the method of relaxation.
keyword(s): Bifurcation , Boundary-value problems , Approximation , Equations , Relaxation (Physics) , Eigenvalues AND Nonlinear systems ,
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| contributor author | W.-C. Xie | |
| date accessioned | 2017-05-09T00:04:02Z | |
| date available | 2017-05-09T00:04:02Z | |
| date copyright | May, 2001 | |
| date issued | 2001 | |
| identifier issn | 0021-8936 | |
| identifier other | JAMCAV-26515#453_1.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/124703 | |
| description abstract | The Lyapunov exponents and moment Lyapunov exponents of a near-nilpotent system under stochastic parametric excitation are studied. The system considered is the linearized system of a two-dimensional nonlinear system exhibiting a pitchfork bifurcation. The effect of stochastic perturbation in the vicinity of static pitchfork bifurcation is investigated. Approximate analytical results of Lyapunov exponent are obtained. The eigenvalue problem for the moment Lyapunov exponent is converted to a two-point boundary value problem, which is solved numerically by the method of relaxation. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | Lyapunov Exponents and Moment Lyapunov Exponents of a Two-Dimensional Near-Nilpotent System | |
| type | Journal Paper | |
| journal volume | 68 | |
| journal issue | 3 | |
| journal title | Journal of Applied Mechanics | |
| identifier doi | 10.1115/1.1364491 | |
| journal fristpage | 453 | |
| journal lastpage | 461 | |
| identifier eissn | 1528-9036 | |
| keywords | Bifurcation | |
| keywords | Boundary-value problems | |
| keywords | Approximation | |
| keywords | Equations | |
| keywords | Relaxation (Physics) | |
| keywords | Eigenvalues AND Nonlinear systems | |
| tree | Journal of Applied Mechanics:;2001:;volume( 068 ):;issue: 003 | |
| contenttype | Fulltext |