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.
Lyapunov Exponents and Moment Lyapunov Exponents of a Two-Dimensional Near-Nilpotent System
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Nov. 9, 1999; final revision, Nov. 8, 2000. Associate Editor: A. A. Ferri. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Xie, W. (November 8, 2000). "Lyapunov Exponents and Moment Lyapunov Exponents of a Two-Dimensional Near-Nilpotent System ." ASME. J. Appl. Mech. May 2001; 68(3): 453–461. https://doi.org/10.1115/1.1364491
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