A Study of the Forced Van der Pol Generalized Oscillator with the Renormalization Group Method
نویسندگان
چکیده
منابع مشابه
Chaos Suppression in Forced Van Der Pol Oscillator
This paper presents a new method of controlling chaos in the nonlinear Van Der Pol oscillator with uncertainties. The proposed method is based on a nonlinear observer to estimate unmeasured velocity signal coupled to a control law. The observer ensures, firstly, an asymptotic convergence of the velocity estimation error. Then, the control law, which is based on the estimated variables, forces 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 کاملStudy on van der Pol Oscillator under Noisy Parametric Excitation
We calculated Eq. (4) by using the Runge-Kutta method. The attractors obtained by the simulations are shown in Fig. 3(a). We can confirm the generation of periodic and chaotic attractors. In order to investigate the attractors in van der Pol oscillator under noisy parametric excitation in detail, we consider the Poincaré map. The result of the Poincaré map are shown in Fig. 3(b). We can see tha...
متن کاملNonlinear Circuit Analysis in Time and Frequency-domain Example: The Forced Van-der-Pol Oscillator
To predict nonlinear circuit behaviour, harmonic-balance (HB) is a popular and useful frequency-domain technique. But given its mathematical nature, it can only converge to mathematical solutions being harmonically related to the input sources into the circuit. Nevertheless, the mathematical solutions to a nonlinear system do not necessarily need to be harmonically related to the input signals ...
متن کاملFirst Integrals for the Duffing-van Der Pol Type Oscillator
In this article, under certain parametric conditions, we study the first integrals of the Duffing-van der Pol-type oscillator equations which include the van der Pol and the Duffing oscillator systems, as particular cases. After making a series of variable transformations and applying the PrellerSinger method, we find the first integrals of the simplified equations without complicated calculati...
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: Applied Physics Research
سال: 2013
ISSN: 1916-9647,1916-9639
DOI: 10.5539/apr.v5n6p74