Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Journal Article · Sat May 01 00:00:00 EDT 1993 · Journal of Statistical Physics; (United States)

DOI:https://doi.org/10.1007/BF01058437· OSTI ID:6328075

Mamachchivaya, N S ^[1]; Van Roessel, H J ^[2]

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1. Univ. of Illinois, Urbana (United States)
2. Univ. of Alberta, Edmonton (Canada)

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provide that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate Ito equations in amplitudes and phases are obtained in the sense of weak convergence. 14 refs.

• OSTI ID: 6328075
• Journal Information: Journal of Statistical Physics; (United States), Vol. 71:3-4; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MECHANICAL VIBRATIONS
STATISTICAL MECHANICS
POISSON EQUATION
ASYMPTOTIC SOLUTIONS
AMPLITUDES
CONVERGENCE
DEGREES OF FREEDOM
LYAPUNOV METHOD
NOISE
OSCILLATORS
PERTURBATION THEORY
ROTATION
SOUND WAVES
STOCHASTIC PROCESSES
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
MECHANICS
MOTION
PARTIAL DIFFERENTIAL EQUATIONS
661100* - Classical & Quantum Mechanics- (1992-)
661300 - Other Aspects of Physical Science- (1992-)