SELF-OSCILLATIONS DESCRIBED BY THE GENERALIZED VAN DER POL EQUATION
نویسندگان
چکیده
منابع مشابه
Self-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 کاملExceptional Complex Solutions of the Forced Van Der Pol Equation
Consider the equation "v dv du = (1 ? u 2)v + ? u describing the orbits of the forced van der Pol equation " u + (u 2 ? 1) _ u + u = ; " a small parameter, (1) in the phase plane. The authors show the existence of two exceptional solutions corresponding to two conjugate complex exceptional values of the parameter near = 1 which remain close to the slow curve v = ?1=(u + 1) both in the direction...
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 کاملThe Duffing–Van der Pol Equation: Metamorphoses of Resonance Curves
We study dynamics of the Duffing–Van der Pol driven oscillator. Periodic steady-state solutions of the corresponding equation are determined within the Krylov-Bogoliubov-Mitropolsky approach to yield dependence of amplitude on forcing frequency as an implicit function, referred to as resonance curve or amplitude profile. Equations for singular points of resonance curves are solved exactly. We i...
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 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: Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies
سال: 2020
ISSN: 2222-0631
DOI: 10.20998/2222-0631.2020.1.10