scholarly journals Two-Point Block Method for Van der Pol Equation

2020 ◽  
Keyword(s):  
Van Der Pol Equation ◽  
Block Method ◽  
Van Der Pol

NUMERICAL SOLUTION FOR DUFFING-VAN DER POL OSCILLATOR VIA BLOCK METHOD

2020 ◽  
Vol 10 (1) ◽  
pp. 1857-8365
Author(s):  
A. F. Nurullah ◽  
M. Hassan ◽  
T. J. Wong ◽  
L. F. Koo
Keyword(s):  
Numerical Solution ◽  
Van Der Pol Oscillator ◽  
Block Method ◽  
Van Der Pol

scholarly journals On Periodic Perturbations of Asymmetric Duffing–Van-der-Pol Equation

2014 ◽  
Vol 24 (05) ◽  
pp. 1450061 ◽  
Author(s):  
Albert D. Morozov ◽  
Olga S. Kostromina
Keyword(s):  
Saddle Point ◽  
Limit Cycles ◽  
Small Neighborhood ◽  
Integrable Equation ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Periodic Perturbations ◽  
Autonomous Equation ◽  
Nonautonomous Equation ◽  
Time Periodic

Time-periodic perturbations of an asymmetric Duffing–Van-der-Pol equation close to an integrable equation with a homoclinic "figure-eight" of a saddle are considered. The behavior of solutions outside the neighborhood of "figure-eight" is studied analytically. The problem of limit cycles for an autonomous equation is solved and resonance zones for a nonautonomous equation are analyzed. The behavior of the separatrices of a fixed saddle point of the Poincaré map in the small neighborhood of the unperturbed "figure-eight" is ascertained. The results obtained are illustrated by numerical computations.

On Integrating Factors and a Perturbation Method

1995 ◽  
Author(s):  
W. T. van Horssen
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Integrating Factors ◽  
Complete Solutions

Abstract In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations. For new classes of differential equations first integrals or complete solutions can be constructed. Also a perturbation method based on integrating factors can be developed. To show how this perturbation method works the method is applied to the well-known Van der Pol equation.

scholarly journals Study of fractional order Van der Pol equation

2016 ◽  
Vol 28 (1) ◽  
pp. 55-60 ◽  
Author(s):  
V. Mishra ◽  
S. Das ◽  
H. Jafari ◽  
S.H. Ong
Keyword(s):  
Fractional Order ◽  
Van Der Pol Equation ◽  
Van Der Pol

scholarly journals A generalization of Van der Pol equation

2013 ◽  
Vol 8 ◽  
pp. 1723-1726
Author(s):  
Ana-Magnolia Marin-Ramirez ◽  
Ruben-Dario Ortiz-Ortiz ◽  
Joel-Arturo Rodriguez-Ceballos
Keyword(s):  
Van Der Pol Equation ◽  
Van Der Pol

Non-standard reduction of noisy Duffing—van der Pol equation

2001 ◽  
Vol 16 (3) ◽  
pp. 223-245 ◽  
Author(s):  
N. Sri Namachchivaya ◽  
Richard B. Sowers ◽  
Lalit Vedula
Keyword(s):  
Van Der Pol Equation ◽  
Van Der Pol
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