Investigation of bounded solutions of linear irregularly perturbed systems by the method of integral manifolds

1970 ◽  
Vol 21 (3) ◽  
pp. 241-252 ◽  
Author(s):  
Ya. S. Baris ◽  
V. I. Fodchuk
Keyword(s):  
Bounded Solutions ◽  
Integral Manifolds ◽  
Perturbed Systems ◽  
Method Of Integral Manifolds

Efficient decomposition of singularly perturbed systems

2019 ◽  
Vol 14 (4) ◽  
pp. 410 ◽  
Author(s):  
Vladimir Sobolev
Keyword(s):  
Enzyme Kinetics ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Differential Systems ◽  
Integral Manifolds ◽  
Perturbed Systems ◽  
Method Of Integral Manifolds

The problem of the decomposition of singularly perturbed differential systems by the method of integral manifolds is studied and the application of the method to the problems of enzyme kinetics is considered.

scholarly journals ORDER REDUCTION OF OPTIMAL ESTIMATION PROBLEM FOR LANGEVIN EQUATION

2017 ◽  
Vol 18 (3.1) ◽  
pp. 40-53
Author(s):  
M.S. Osintsev
Keyword(s):  
Covariance Matrix ◽  
Langevin Equation ◽  
Order Reduction ◽  
Optimal Estimation ◽  
Theoretical Method ◽  
Estimation Problem ◽  
Lower Dimension ◽  
Integral Manifolds ◽  
Question Under Discussion ◽  
Method Of Integral Manifolds

The question under discussion in this paper is the optimal estimation for singular perturbed Langevin equation. On the basis of assumptions about parameters and conditions where the movement is performed, we choose three cases which have curtain peculiarities during the reduction of the optimal estimation problem. For order reduction task the theoretical method of integral manifolds is used. It allows to get the solution of Riccati equations for covariance matrix of the filter and build the corrected Kalman–Bucy filter of a lower dimension

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