Lyapunov Exponents and Rotation number of Two-Ddimensional Systems with Telegraphic Noise

1 August 1989

journal article
Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics

Vol. 49 (4) , 1242-1274
https://doi.org/10.1137/0149075

Abstract

Exact expressions for the exponential growth rates (Lyapunov exponents) and rotation numbers of two-dimensional systems perturbed by telegraphic noise are derived. Asymptotic expansions for small, large, slow, and fast noise and the white noise limit are constructed. Then results are applied to the random oscillator, stochastic stability (in particular, stabilization by noise) and stochastic bifurcation.

Keywords

This publication has 14 references indexed in Scilit:

Large deviations of linear stochastic differential equations
Published by Springer Nature ,2006
Lyapunov Exponents of Nonlinear Stochastic Systems
Published by Springer Nature ,1988
Recurrence and Invariant Measures for Degenerate Diffusions
The Annals of Probability, 1987
Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications
SIAM Journal on Applied Mathematics, 1986
Markov Processes
Published by Wiley ,1986
Lyapunov exponents of linear stochastic systems
Lecture Notes in Mathematics, 1986
Lyapunov Exponents
Published by Springer Nature ,1986
Noise Induced Transitions
Published by Springer Nature ,1984
Stabilization of Linear Systems by Noise
SIAM Journal on Control and Optimization, 1983
Qualitative Theory of Stochastic Systems
Published by Elsevier ,1983