Symmetry induced oscillations in four-dimensional models deriving from the van der Pol equation
نویسندگان
چکیده
منابع مشابه
Symmetry induced Dynamics in four-dimensional Models deriving from the van der Pol Equation
Different models of self-excited oscillators which are four-dimensional extensions of the van der Pol system are reported. Their symmetries are analyzed. Three of them were introduced to model the release of vortices behind circular cylinders with a possible transition from a symmetric to an antisymmetric Bénard-von Karman vortex street. The fourth reported self-excited oscillator is a new mode...
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 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 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 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: Chaos, Solitons & Fractals
سال: 2004
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2003.09.033