  Limit cycles (attractors for neighbouring periodic orbits in a dissipative
dynamical system) have been widely studied but the corresponding generalization
for quasi periodic orbits have rarely been discussed. Here we investigate
"higher dimensional limit cycles" by analysing a pair of coupled non identical
Van der Pol oscillators and also the Kuznetsov oscillator. We find that the
renormalization group based approach introduced by Chen, Goldenfeld and Oono is
ideally suited for analysing the quasi periodic analogues of limit cycles. We
also address entrainment issues in a pair of forced and coupled Van der Pol
oscillators. Our principle finding there is that if two such independent
oscillators one with frequency entrainment and the other without are coupled
linearly, then it is possible to produce an entrained state via the coupling.
