Efficient decomposition of singularly perturbed systems

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.

ORDER REDUCTION OF OPTIMAL ESTIMATION PROBLEM FOR LANGEVIN EQUATION

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

Nonlinear Behavior of Flutter Unstable Dynamical Systems With Gyroscopic and Circulatory Forces

Postflutter behavior of nonlinear discrete dynamical systems having a combination of gyroscopic and circulatory forces are studied. The study leads to Hopf bifurcations. The method of analysis is based on the method of Hopf and the method of integral manifolds. The results of the analysis are applied to an example and the accuracy of the analysis is checked against numerical solutions of the equations of motion.