The equation $y' = -2\sin(2\pi y)$ has stable fixed points when $y$ is an integer. Let us add some noise, so that we have $$ y' = -2\sin(2\pi y) + f, $$ where $f$ is a random function. This gives us a process that hops from one fixed point to another. We illustrate first for $t\in [0,100]$ with $\lambda = 0.4$.

rng(0), dom = [0 100]; tic
N = chebop(dom);
lambda = 0.4; f = randnfun(lambda,dom,'norm');
N.op = @(y) diff(y) + 2*sin(2*pi*y); N.lbc = 0;
LW = 'linewidth'; FS = 'fontsize';
y = N\f; plot(y,LW,2), grid on
xlabel('t',FS,32), ylabel('y',FS,32)

Here we cut $\lambda$ in half.

lambda = lambda/2;
f = randnfun(lambda,dom,'norm');
y = N\f; plot(y,LW,1), grid on
xlabel('t',FS,32), ylabel('y',FS,32)

total_time_in_seconds = toc

total_time_in_seconds =
  18.500097000000000