Limit Cycles Close to Infinity of Certain Non-Linear Differential Equations

1990 ◽  
Vol 33 (1) ◽  
pp. 55-59
Author(s):  
Víctor Guíñez ◽  
Eduardo Sáez ◽  
Iván Szántó
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Limit Cycles ◽  
Linear Differential Equations ◽  
Polynomial Vector ◽  
Polynomial Vector Field ◽  
Non Linear ◽  
Linear Differential

AbstractThrough successive radial perturbations of a certain planar Hamiltonian polynomial vector field of degree 2K + 1, we obtain a least K limit cycles containing (2K + 1)2 singularities.

scholarly journals Zero Counting and Invariant Sets of Differential Equations

2017 ◽  
Vol 2019 (13) ◽  
pp. 4119-4158
Author(s):  
Gal Binyamini
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Upper Bound ◽  
Linear Differential Equations ◽  
Invariant Sets ◽  
Polynomial Vector ◽  
Algebraic Hypersurface ◽  
Polynomial Differential Equations ◽  
Polynomial Vector Field ◽  
Linear Differential

Abstract Consider a polynomial vector field $\xi$ in ${\mathbb C}^n$ with algebraic coefficients, and $K$ a compact piece of a trajectory. Let $N(K,d)$ denote the maximal number of isolated intersections between $K$ and an algebraic hypersurface of degree $d$. We introduce a condition on $\xi$ called constructible orbits and show that under this condition $N(K,d)$ grows polynomially with $d$. We establish the constructible orbits condition for linear differential equations over ${\mathbb C}(t)$, for planar polynomial differential equations and for some differential equations related to the automorphic $j$-function. As an application of the main result, we prove a polylogarithmic upper bound for the number of rational points of a given height in planar projections of $K$ following works of Bombieri–Pila and Masser.

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

scholarly journals Pendulum with aerodynamic and viscous damping

2020 ◽  
Vol 3 (2) ◽  
pp. 43-47
Author(s):  
Herlin Soraya
Keyword(s):  
Differential Equations ◽  
Stable State ◽  
The State ◽  
Linear Differential Equations ◽  
Viscous Damping ◽  
Viscous Damper ◽  
Aerodynamic Damping ◽  
Non Linear ◽  
Linear Differential ◽  
The Relationship

In this paper we discuss about how the relationship between non-linear differential equations on aerodynamic damping with linearly viscous damping equations. And it turns out after analyzing that the changes that occur pendulum that changes from the start of the maximum state to a stable state takes time so that changes that occur until the state is stable, this change can be reduced with the use of viscous damper

scholarly journals Boundedness of Solutions for Second Order Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

We present new theorems which specify sufficient conditions for the boundedness of all solutions for second order non-linear differential equations. Unboundedness of solutions is also considered.

scholarly journals Modelling of a non-linear coil with loss in iron using the Runge-Kutta methods

2016 ◽  
Vol 65 (3) ◽  
pp. 527-539 ◽  
Author(s):  
Joanna Kolańska-Płuska ◽  
Barbara Grochowicz
Keyword(s):  
Differential Equations ◽  
State Space ◽  
Linear Differential Equations ◽  
Non Linear ◽  
Runge Kutta ◽  
Linear Differential ◽  
Space Description

Abstract This work presents a study on dynamics of a circuit with a non-linear coil, where loss in iron is also taken into account. A coil model is derived using a state space description. The work also includes the development of an application in C# for coil dynamics examination, where the implicit RADAU IIA method of various orders is applied for the purpose of solving non-linear differential equations modelling the non-linear coil with loss in iron.

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