Open AccessResponse to bounded noise excitation of stochastic Mathieu-Duffing system with time delay state feedback
Author(s) -
Xing Zhen-Ci,
Wei Xu,
Rong Hai-Wu,
Wang Bao-Yan
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.824
Subject(s) - parametric statistics , mathieu function , bifurcation , excitation , duffing equation , control theory (sociology) , amplitude , bounded function , stability (learning theory) , physics , mathematics , mathematical analysis , nonlinear system , computer science , quantum mechanics , statistics , control (management) , artificial intelligence , machine learning
We investigate the principal parametric resonance of Mathieu-Duffing Equation under a narrow-band random excitation with time delay feedback. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The bifurcation of the system is discussed. We find that the bifurcation can be influenced by the detuning parameter, time delay, and the intensity of the non-linear term, and an appropriate choice of these parameters can change the response of bifurcation. In addition the stability of nontrivial solution is studied. The nontrivial solution of necessary and sufficient condition for stability is obtained. Moreover, we find that when the bandwidth of the random excitation is smaller, the multi-solution phenomenon still exists, and bifurcation and jumping phenomenon will occur. Theoretical analysis is verified by numerical results.