Construction of approximate periodic solutions to a modified van der Pol oscillator

被引：7
|
作者：
Marinca, V. [1 ]
Draganescu, G. E. [1 ]
机构：
[1] Polytech Univ Timisoara, Dept Mech & Vibrat, Timisoara 300222, Romania
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 05期
关键词：
Iteration procedure; Approximate method; Modified van der Pol equation; Periodic solution; Nonlinear oscillation; ITERATION PERTURBATION METHOD; NONLINEAR OSCILLATORS; LIMIT-CYCLE;
D O I：
10.1016/j.nonrwa.2010.05.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new iteration scheme is proposed and applied for the modified van der Pol oscillator. A simple and effective iteration procedure to search for the periodic solutions of the equation is given. This procedure is a powerful tool for the determination of the approximate frequencies and periodic solutions of the nonlinear differential equations. The solutions obtained using the present iteration procedure are in good agreement with the numerical integration obtained by a fourth order Runge-Kutta method, which shows the applicability of the procedure. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：4355 / 4362
页数：8
相关论文
共 50 条
  • [1] Periodic Solutions in the van der Pol Oscillator: A Comparison
    Bares, Cinthya A.
    Moiola, Jorge L.
    Calandrini, Guillermo L.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2025,
  • [2] THE MODIFIED VAN DER POL OSCILLATOR
    ROBINSON, FNH
    IMA JOURNAL OF APPLIED MATHEMATICS, 1987, 38 (02) : 135 - 150
  • [3] PERIODIC MOTIONS IN A VAN DER POL OSCILLATOR
    Xu, Yeyin
    Luo, Albert C. J.
    PROCEEDINGS OF THE ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, 2018, VOL 4B, 2019,
  • [4] Rapidly and Slowly Oscillating Periodic Solutions of a Delayed Van der Pol Oscillator
    Gabor Kiss
    Jean-Philippe Lessard
    Journal of Dynamics and Differential Equations, 2017, 29 : 1233 - 1257
  • [5] On the periodic solutions of a generalized non-linear Van der Pol oscillator
    Waluya, SB
    van Horssen, WT
    JOURNAL OF SOUND AND VIBRATION, 2003, 268 (01) : 209 - 215
  • [6] Rapidly and Slowly Oscillating Periodic Solutions of a Delayed Van der Pol Oscillator
    Kiss, Gabor
    Lessard, Jean-Philippe
    JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2017, 29 (04) : 1233 - 1257
  • [7] Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol system
    Zhang, Yanni
    Zhao, Zhen
    Pang, Jing
    JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, 2023, 42 (03) : 1312 - 1318
  • [8] PERIODIC SOLUTIONS OF VAN DER POL EQUATION
    ZONNEVELD, JA
    KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETESCHAPPEN-PROCEEDINGS SERIES A-MATHEMATICAL SCIENCES, 1966, 69 (05): : 620 - +
  • [9] Stability analysis for periodic solutions of the Van der Pol-Duffing forced oscillator
    Cui, Jifeng
    Liang, Jiaming
    Lin, Zhiliang
    PHYSICA SCRIPTA, 2016, 91 (01)
  • [10] Nonlinear analysis in a modified van der Pol oscillator
    Braga, Denis de Carvalho
    de Faria, Nivaldo Goncalves
    Mello, Luis Fernando
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 245 : 474 - 486
12345