scholarly journals Study of limit cycles of an autonomous system of differential equations

1972 ◽  
Vol 7 (2) ◽  
pp. 309-311
Author(s):  
R.F. Matlak
Keyword(s):  
Differential Equations ◽  
Limit Cycles ◽  
Autonomous System ◽  
System Of Differential Equations

scholarly journals On acyclicity of quadratic system with two non-rough foci

2021 ◽  
pp. 41-46
Author(s):  
Адам Дамирович Ушхо
Keyword(s):  
Differential Equations ◽  
Limit Cycles ◽  
Phase Plane ◽  
Second Order ◽  
Quadratic System ◽  
Equilibrium States ◽  
System Of Differential Equations ◽  
Right Hand ◽  
The Right

Доказывается, что система дифференциальных уравнений, правые части которой представляют собой полиномы второй степени, не имеет предельных циклов, если в ограниченной части фазовой плоскости она имеет только два состояния равновесия и при этом они являются состояниями равновесия второй группы. It is proved that a system of differential equations, the right-hand sides of which are second-order polynomials, has no limit cycles if it has only two equilibrium states in the bounded part of the phase plane, and they are the equilibrium states of the second group.

scholarly journals On constructing single-input non-autonomous systems of full rank

2018 ◽  
Keyword(s):  
Vector Field ◽  
Nonlinear System ◽  
Differential Equations ◽  
Autonomous System ◽  
Vector Fields ◽  
Autonomous Systems ◽  
Full Rank ◽  
System Of Differential Equations ◽  
Single Input ◽  
Class C

For a nonlinear system of differential equations $\dot x=f(x)$, a method of constructing a system of full rank $\dot x=f(x)+g(x)u$ is studied for vector fields of the class $C^k$, $1\le k<\infty$, in the case when $f(x)\not=0$. A method for constructing a non-autonomous system of full rank is proposed in the case when the vector field $f(x)$ can vanish.

scholarly journals An autonomous system of differential equations in the plane

1969 ◽  
Vol 1 (3) ◽  
pp. 391-395 ◽  
Author(s):  
R.F. Matlak
Keyword(s):  
Differential Equations ◽  
Autonomous System ◽  
Present Note ◽  
Geometric Features ◽  
System Of Differential Equations ◽  
New Approach

In the present note the equation yn = x1-m ym is reduced, under appropriate conditions, to a quadratic autonomous system of differential equations in the plane. In pursuance of this new approach, the main geometric features of this autonomous system are determined and a method of solving it is outlined.

ENERGY EIGENVALUE LEVEL MOTION AND A SYMBOLICC++ IMPLEMENTATION

2000 ◽  
Vol 11 (07) ◽  
pp. 1347-1356
Author(s):  
WILLI-HANS STEEB ◽  
YORICK HARDY
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Discrete Spectrum ◽  
Autonomous System ◽  
Energy Eigenvalue ◽  
System Of Differential Equations ◽  
Eigenvalues And Eigenvectors ◽  
Hamilton Operator ◽  
Energy Eigenvalues

We consider the Hamilton operator [Formula: see text]. We assume that [Formula: see text] has a discrete spectrum. We show that the energy eigenvalues and eigenvectors obey an autonomous system of ordinary differential equations. An implementation of this system of differential equations is given using SymbolicC++.

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