Differential Equation
We use x_1 (t)
and x_2 (t)
to denote the oscillator position and velocity as a function of time.
The ordinary differential equation for the
Van der Pol oscillator with no noise satisfies the differential equation
\[
\begin{array}{rcl}
x_1 '(t) & = & x_2 (t)
\\
x_2 '(t) & = & \mu [ 1 - x_1(t)^2 ] x_2 (t) - x_1(t)
\end{array}
\]
mu
Is a scalar specifying the value of \mu
is the
differential equation above.
xi
is a column vector with two elements specifying the initial value for
x(t) \in \B{R}^2
.
To be specific, x_1 (0)
is equal to
xi(1)
and
x_2(0)
is equal to
xi(2)
.
n_out
is an integer scalar that specifies the number of time points at which
the approximate solution to the ODE is returned.
step
is a scalar that specifies the difference in time between points at which
the solution of the ODE is approximated.
x_out
is a matrix with row size two and column size
n_out
that
contains the approximation solution to the ODE.
To be specific, for
k = 1 , ... , n_out
,
x_out(i,k)
is an approximation for
x_i [ (k-1) \Delta t ]
.
Method
A fourth-order Runge method with step size
step
is used
to approximate the solution of the ODE.
Example
The file vanderpol_sim_ok.m
is an example and test
of vanderpol_sim.
It returns true, if the test passes, and false otherwise.
Input File: example/nonlinear/vanderpol_sim.m
