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.

Issue Section:
Technical Papers
Keywords:
bifurcation, Lyapunov methods, elasticity, mechanical stability, vibrations, stochastic processes, damping
Topics:
Approximation, Bifurcation, Boundary-value problems, Eigenvalues, Damping, Relaxation (Physics)
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