  We study the behaviour of the van der Pol oscillator when either its damping
parameter $\mu$ or its nonlinearity parameter $\xi$ is subject to additive or
multiplicative random noise. Assuming various power law exponents for the
relation between the oscillating variable and the sunspot number, for each case
we map the parameter plane defined by the amplitude and the correlation time of
the perturbation and mark the parameter regime where the sunspot number
displays solar-like behaviour. Solar-like behaviour is defined here as a good
correlation between the rise rate and cycle amplitude {\it and} the lack of a
good correlation between the decay rate and amplitude, together with
significant ($\ga 10$\,%) r.m.s. variation in cycle lengths and cycle
amplitudes. It is found that perturbing $\mu$ alone the perturbed van der Pol
oscillator does not show solar-like behaviour. When the perturbed variable is
$\xi$, solar-like behaviour is displayed for perturbations with a correlation
time of about 3--4 years and significant amplitude. Such studies may provide
useful constraints on solar dynamo models and their parameters.
