van der pol Definition and 7 Threads

First i looked at the case of ## \epsilon = 0## and came to the conclusion, that this oscillator has a circular limit cycle in a phase space trajectory, when plotted with the axes x and ##\dot{x}##. I have found that ##x_0^p (t) = a_1 \cos(t)## which implies that all other Fourier- coefficients...

The van der pol non-linear equation is given as-: y''=A(1-y²)y'-By y=amplitude The analysis given by the book is this-: When y²<1 i.e when y is small A(1-y²) is negative. A(1-y²) is called damping term. I don't understand how is it negative? It obviously becomes positive in this case...

Homework Statement Given characteristic equation for a circuit containing a diode, I must figure out how to fit a polynomial to the curve so that the van der pol equation is obtained. The paper I am reading is here: http://www.unige.ch/math/hairer60/pres/pres_rentrop.pdf My doubts are...

Homework Statement As the title says, I am trying to implement two differential equations into Simulink. I don't know how to start. How do I know what to start with, which block goes where? when do I add something and when do I know to subtract something using the sum block. When I got my...

$$ x'' + \varepsilon(x^2-1)x'+x=0\quad \varepsilon\ll 1 $$ Using multiple scale perturbation and letting $f(x,x') = (x^2-1)x'$, we have $$ x_{0tt} + \varepsilon x_{1tt} + 2\varepsilon x_{0tT} + \cdots + \varepsilon f(x_0,x_{0t}) + \cdots + x_0 + \varepsilon x_1 + \cdots = 0 $$ where $T$ is our...

Homework Statement Consider the biased van der Pol oscillator: \frac{d^2x}{dt^2}=u (x^2-1)\frac{dx}{dt} + x = a. Find the curves in (u,a) space at which Hopf bifurcations occur. (Strogatz 8.21) Homework Equations The Attempt at a Solution Not even sure where to start with this...

Hello guys, I am looking for the original article of Van der Pol. B. van der Pol, "The nonlinear theory of electric oscillations," Proc. IRE, vol. 22, pp. 1051--1086, Sept. 1934. do you have an idea of where i can find it? (online :blushing:, or what does proc. IRE means?) The main...