We study the propagation of nonlinear MHD waves in a highly magnetized
dissipative plasma cavity forced at its boundaries. This interacting
wave system is analyzed by Galerkin and multiple-scale analyses leadin
g to a simple dynamical system which shares the properties of both the
van der Pol and the Duffing oscillator. The system is separated into
a Hamiltonian part - possessing a double homoclinic loop to a saddle -
and a perturbation. By means of the Melnikov function technique, we s
how that the saddle's stable and unstable manifolds intersect for suit
able values of the forcing amplitude, provided the forcing frequency e
xceeds a critical value. Saddle-node and period-doubling sequences of
bifurcations of periodic orbits (notably a period-three orbit) set in
near the homoclinic intersection; these accumulate from below to the s
ame critical value of the control parameter, at which a chaotic limit
set appears with fractal dimension similar or equal to 2.25. Beyond th
is critical value chaos unfolds into periodic orbits, via saddlenode-b
ifurcations. Near one of these, the Alfven wave's amplitude has an int
ermittent behaviour over long time-scales with a power chute of about
90% at the intermissions.