A fuzzy crisis in a Duffing-van der Pol system

被引：7
|
作者：
Hong Ling [1 ]
机构：
[1] Xi An Jiao Tong Univ, MOE Key Lab Strength & Vibrat, Xian 710049, Peoples R China
来源：
CHINESE PHYSICS B | 2010年 / 19卷 / 03期
基金：
中国国家自然科学基金;
关键词：
fuzzy dynamical systems; fuzzy noise; fuzzy bifurcation; cell mapping methods; GLOBAL ANALYSIS; BIFURCATIONS; ATTRACTORS; DYNAMICS;
D O I：
10.1088/1674-1056/19/3/030513
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
A crisis in a Duffing-van del Pol system with fuzzy uncertainties is studied by means of the fuzzy generalised cell mapping (FGCM) method. A crisis happens when two fuzzy attractors collide simultaneously with a fuzzy saddle on the basin boundary as the intensity of fuzzy noise reaches a critical point. The two fuzzy attractors merge discontinuously to form one large fuzzy attractor after a crisis. A fuzzy attractor is characterized by its global topology and membership function. A fuzzy saddle with a complicated pattern of several disjoint segments is observed in phase space. It leads to a discontinuous merging crisis of fuzzy attractors. We illustrate this crisis event by considering a fixed point under additive and multiplicative fuzzy noise. Such a crisis is fuzzy noise-induced effects which cannot be seen in deterministic systems.
引用
收藏
页数：6
相关论文
共 50 条
  • [21] Control and synchronization in the Duffing-van der Pol and F6 Duffing oscillators
    Uriostegui-Legorreta, U.
    Tututi, E. S.
    INDIAN JOURNAL OF PHYSICS, 2023, 97 (14) : 4303 - 4315
  • [22] Stochastic averaging on graphs: Noisy Duffing-van der Pol equation
    Namachchivaya, NS
    Sowers, R
    Vedula, L
    STOCHASTIC AND CHAOTIC DYNAMICS IN THE LAKES, 2000, 502 : 255 - 265
  • [23] Statistical dynamics at critical bifurcations in Duffing-van der Pol oscillator
    Chinnathambi, V
    Rajasekar, S
    PRAMANA-JOURNAL OF PHYSICS, 1999, 52 (06): : 561 - 577
  • [24] Response of a stochastic Duffing-Van der Pol elastic impact oscillator
    Wang, Liang
    Xu, Wei
    Li, Gaojie
    Li, Dongxi
    CHAOS SOLITONS & FRACTALS, 2009, 41 (04) : 2075 - 2080
  • [25] Resonance Analysisfor Weakly Nonlinear Duffing-van der Pol Oscillation
    Chen, Songlin
    Wang, Nannan
    IAENG International Journal of Applied Mathematics, 2024, 54 (02) : 238 - 242
  • [26] Statistical dynamics at critical bifurcations in Duffing-van der Pol oscillator
    V. Chinnathambi
    S. Rajasekar
    Pramana, 1999, 52 : 561 - 577
  • [27] HOMOTOPY PERTURBATION METHOD TO SOLVE DUFFING-VAN DER POL EQUATION
    Moussa, Bagayogo
    Youssouf, Minoungou
    Wassiha, Nebie Abdoul
    Youssouf, Pare
    ADVANCES IN DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES, 2024, 31 (03): : 299 - 315
  • [28] Complex Dynamics in a Duffing-Van der Pol Oscillator with φ6 Potential
    Yu, Jun
    Xie, Zhi-kun
    Yu, Li-xian
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2008, 77 (11)
  • [29] Stochastic stability and control of coupled Duffing-van der Pol systems
    Li, W
    Xu, W
    Zhao, JF
    Jin, YF
    ACTA PHYSICA SINICA, 2005, 54 (12) : 5559 - 5565
  • [30] Lyapunov exponents and stability for the stochastic duffing-van der Pol oscillator
    Baxendale, PH
    IUTAM SYMPOSIUM ON NONLINEAR STOCHASTIC DYNAMICS, 2003, 110 : 125 - 135
12345