Asymptotic decomposition of differential systems with a small parameter

1987 ◽  
Vol 39 (2) ◽  
pp. 162-170
Author(s):  
Yu. A. Mitropol'skii ◽  
A. K. Lopatin
Keyword(s):  
Small Parameter ◽  
Asymptotic Decomposition ◽  
Differential Systems

scholarly journals ON THE NUMBER OF LIMIT CYCLES FOR DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN ℝ2n WITH TWO ZONES

2013 ◽  
Vol 23 (02) ◽  
pp. 1350024 ◽  
Author(s):  
JAUME LLIBRE ◽  
FENG RONG
Keyword(s):  
Small Parameter ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Displacement Function ◽  
Averaging Theory ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Order Expansion ◽  
Linear Differential

We study the number of limit cycles of the discontinuous piecewise linear differential systems in ℝ2n with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result, we use the averaging theory in a form where the differentiability of the system is not necessary.

scholarly journals REDUCTION OF MATHEMATICAL MODEL OF ROBOT WITH ELASTIC JOINTS

2017 ◽  
Vol 20 (3) ◽  
pp. 20-33
Author(s):  
O.V. Vidilina ◽  
N.V. Voropaeva
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Integral Manifold ◽  
Singularly Perturbed ◽  
Slow Movement ◽  
Parameter System ◽  
Asymptotic Decomposition ◽  
Differential Systems ◽  
Small Dissipation ◽  
Elastic Joints

A model of n - joint manipulator with elastic joints with small dissipation is studied. Class of singularly perturbed differential systems that describe the dynamics of robot is singled out. For a given class of systems the existence and uniqueness of integral manifoldness of slow movement is established, its features are studied. It is proved that integral manifold may be constructed with any degree of accuracy as asymptotic decomposition inpowers of small parameter. System that is used to describe movement in manifolds may be used as a reduced model of initial system.

ASYMPTOTIC METHODS FOR MICROPOLAR FLUIDS IN A TUBE STRUCTURE

2004 ◽  
Vol 14 (05) ◽  
pp. 735-758 ◽  
Author(s):  
D. DUPUY ◽  
G. P. PANASENKO ◽  
R. STAVRE
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansion ◽  
Small Parameter ◽  
Asymptotic Methods ◽  
Steady Motion ◽  
Asymptotic Decomposition ◽  
Micropolar Fluids ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Tube Structure

The steady motion of a micropolar fluid through a wavy tube with the dimensions depending on a small parameter is studied. An asymptotic expansion is proposed and error estimates are proved by using a boundary layer method. We apply the method of partial asymptotic decomposition of domain and we prove that the solution of the partially decomposed problem represents a good approximation for the solution of the considered problem.

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