Analysis of a fractional order Van der Pol-like oscillator via describing function method

被引：32
|
作者：
Attari, Mina [1 ]
Haeri, Mohammad [1 ]
Tavazoei, Mohammad Saleh [1 ]
机构：
[1] Sharif Univ Technol, Dept Elect Engn, Adv Control Syst Lab, Tehran, Iran
来源：
NONLINEAR DYNAMICS | 2010年 / 61卷 / 1-2期
关键词：
Fractional Van der Pol oscillator; Describing function method; Oscillatory parametric region; Harmonic balance; SINUSOIDAL OSCILLATORS; STABILITY ANALYSIS; SYSTEMS; CHAOS; IDENTIFICATION;
D O I：
10.1007/s11071-009-9647-0
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, the behavior of a fractional order Van der Pol-like oscillator is investigated using a describing function method. A parametric function for the boundary between oscillatory and nonoscillatory regions of this system is extracted. The analytical results are evaluated by numerical simulations which demonstrate sufficient reliability of the proposed analyzing method.
引用
收藏
页码：265 / 274
页数：10
相关论文
共 50 条
  • [41] Numerical Solution of the Fractional Order Duffing–van der Pol Oscillator Equation by Using Bernoulli Wavelets Collocation Method
    Rahimkhani P.
    Moeti R.
    International Journal of Applied and Computational Mathematics, 2018, 4 (2)
  • [42] Complex-order forced van der Pol oscillator
    Pinto, Carla M. A.
    Tenreiro Machado, J. A.
    JOURNAL OF VIBRATION AND CONTROL, 2012, 18 (14) : 2201 - 2209
  • [43] Complex-order forced van der Pol oscillator
    Pinto, Carla M.A.
    MacHado, J.A. Tenreiro
    JVC/Journal of Vibration and Control, 2012, 18 (14): : 2201 - 2209
  • [44] Bifurcation and stability analysis of commensurate fractional-order van der Pol oscillator with time-delayed feedback
    Chen, Jufeng
    Shen, Yongjun
    Li, Xianghong
    Yang, Shaopu
    Wen, Shaofang
    INDIAN JOURNAL OF PHYSICS, 2020, 94 (10) : 1615 - 1624
  • [45] Bifurcation and stability analysis of commensurate fractional-order van der Pol oscillator with time-delayed feedback
    Jufeng Chen
    Yongjun Shen
    Xianghong Li
    Shaopu Yang
    Shaofang Wen
    Indian Journal of Physics, 2020, 94 : 1615 - 1624
  • [46] Understanding Injection Locking and Synchronization with Van der Pol-Like Self-sustained Oscillators
    Enrique Beltran-Gonzalez, Luis
    Quintero-Bermudez, Rafael
    Quintero-Torres, Rafael
    CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2020, 39 (10) : 4775 - 4791
  • [47] Asymptotic solution of the van der Pol oscillator with small fractional damping
    Xie, Feng
    Lin, Xueyuan
    PHYSICA SCRIPTA, 2009, T136
  • [48] Crises of a Fractional Birhythmic Van der Pol Oscillator Using the Improved Cell Mapping Method
    Yuan, Minjuan
    Xu, Wei
    Wang, Liang
    Lu, Yisha
    Peng, Jiahui
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2024, 34 (08):
  • [49] 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
  • [50] The Residue Harmonic Balance Method for Duffing-Van Der Pol Oscillator with Fractional Derivative
    Xue, Xin
    Li, Lianzhong
    Sun, Dan
    ADVANCED TECHNOLOGIES IN MANUFACTURING, ENGINEERING AND MATERIALS, PTS 1-3, 2013, 774-776 : 103 - 106
12345