Discretization of a Random Dynamical System near a Hyperbolic Point

DOI10.1002/mana.3211810103zbMath0857.34058OpenAlexW1967034268MaRDI QIDQ4892476

Ludwig Arnold, Peter E. Kloeden

Publication date: 6 March 1997

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.3211810103

zbMATH Keywords

noiseconsistencydiscretization errorone-step numerical methodgeneral nonlinear systemrandom system of differential equationssmall random perturbations of a deterministic hyperbolic point

Mathematics Subject Classification ID

Stochastic stability in control theory (93E15) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Ordinary differential equations and systems with randomness (34F05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Probabilistic methods, stochastic differential equations (65C99)

Related Items

Shadowing orbits of a class of random differential equations ⋮ Multivalued perturbations of a saddle dynamics ⋮ The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations ⋮ The local linearization method for numerical integration of random differential equations

Cites Work

• A stochastic version of center manifold theory
• Center manifolds of dynamical systems under discretization
• Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications
• On the Numerical Approximation of Phase Portraits Near Stationary Points
• Approximation of Upper Lyapunov Exponents of Bilinear Stochastic Differential Systems
• Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations