Asymptotic analysis of kinematically excited dynamical systems near resonances

2011 ◽  
Vol 68 (4) ◽  
pp. 459-469 ◽  
Author(s):  
Roman Starosta ◽  
Grażyna Sypniewska-Kamińska ◽  
Jan Awrejcewicz
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Analysis

scholarly journals APPROXIMATION OF INVARIANT FOLIATIONS FOR STOCHASTIC DYNAMICAL SYSTEMS

2012 ◽  
Vol 12 (01) ◽  
pp. 1150011 ◽  
Author(s):  
XU SUN ◽  
XINGYE KAN ◽  
JINQIAO DUAN
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Analysis ◽  
Nonlinear Dynamical Systems ◽  
Random Sets ◽  
Stochastic Dynamical Systems ◽  
Geometric Structures ◽  
Nonlinear Dynamical

Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random sets. Thus it is desirable to have some techniques to approximate random invariant foliations. In this paper, invariant foliations are approximated for dynamical systems with small noisy perturbations, via asymptotic analysis. Namely, random invariant foliations are represented as a perturbation of the deterministic invariant foliations, with deviation errors estimated.

Sign in / Sign up

Export Citation Format

Share Document