Oscillations in a van der Pol equation with delayed argument
نویسندگان
چکیده
منابع مشابه
Double Hopf bifurcation in delayed van der Pol-Duffing equation
In this paper, we study dynamics in delayed van der Pol–Duffing equation, with particular attention focused on nonresonant double Hopf bifurcation. Both multiple time scales and center manifold reduction methods are applied to obtain the normal forms near a double Hopf critical point. A comparison between these two methods is given to show their equivalence. Bifurcations are classified in a two...
متن کاملA new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition method
In this article, a new method is introduced to give approximate solution to Van der Pol equation. The proposed method is based on the combination of two different methods, the spectral Adomian decomposition method (SADM) and piecewise method, called the piecewise Adomian decomposition method (PSADM). The numerical results obtained from the proposed method show that this method is an...
متن کاملPeriodic solutions for van der Pol equation with time delay
In this paper, the van der Pol equation with a time delay is considered, where the time delay is regarded as a parameter. It is found that Hopf bifurcation occurs when this delay passes through a sequence of critical value. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manif...
متن کاملSelf-sustained current oscillations in superlattices and the van der Pol equation
Z. Z. Sun, J. P. Cao, 2 Sun Yin, Y. P. Wang, Y. Q. Wang, and X. R. Wang ∗ Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China Institute of Physics & Center for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, P.R. China Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, P.R. China (Dated: Septembe...
متن کاملQuasiperiodic phenomena in the Van der Pol - Mathieu equation
The Van der Pol Mathieu equation, combining self-excitation and parametric excitation, is analysed near and at 1 : 2 resonance, using the averaging method. We analytically prove the existence of stable and unstable periodic solutions near the parametric resonance frequency. Above a certain detuning threshold, quasiperiodic solutions arise with basic periods of order 1 and order 1/ε where ε is t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2002
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(02)00422-5