Random perturbations of dynamical systems with reflecting boundary and corresponding PDE with a small parameter

2014 ◽  
Vol 88 (4) ◽  
pp. 187-200
Author(s):  
Wenqing Hu ◽  
Lucas Tcheuko
Keyword(s):  
Dynamical Systems ◽  
Small Parameter ◽  
Random Perturbations

scholarly journals Second-order differential equations with random perturbations and small parameters

2017 ◽  
Vol 147 (4) ◽  
pp. 763-779
Author(s):  
M. Kamenskii ◽  
S. Pergamenchtchikov ◽  
M. Quincampoix
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Random Perturbation ◽  
Stochastic Averaging ◽  
Second Order ◽  
Random Perturbations ◽  
Existence And Uniqueness Theorem ◽  
Second Order Differential Equations ◽  
Averaging Theorem ◽  
Small Parameters

We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero.

Symplectic analysis of dynamical systems with a small parameter. A new criterion for stabilization of homoclinic separatrices and its application

1992 ◽  
Vol 44 (1) ◽  
pp. 41-58
Author(s):  
Yu. O. Mitropol'skii ◽  
I. O. Antonishin ◽  
A. K. Prikarpats'kyy ◽  
V. G. Samoilenko
Keyword(s):  
Dynamical Systems ◽  
Small Parameter ◽  
New Criterion

Persistence of Dynamical Systems under Random Perturbations

SIAM Review ◽  
1975 ◽  
Vol 17 (4) ◽  
pp. 605-640 ◽  
Author(s):  
Donald Ludwig
Keyword(s):  
Dynamical Systems ◽  
Random Perturbations
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