  We study the effects of intrinsic noise on chemical reaction systems, which
in the deterministic limit approach a limit cycle in an oscillatory manner.
Previous studies of systems with an oscillatory approach to a fixed point have
shown that the noise can transform the oscillatory decay into sustained
coherent oscillations with a large amplitude. We show that a similar effect
occurs when the stable attractors are limit cycles. We compute the correlation
functions and spectral properties of the fluctuations in suitably co-moving
Frenet frames for several model systems including driven and coupled
Brusselators, and the Willamowski-Roessler system. Analytical results are
confirmed convincingly in numerical simulations. The effect is quite general,
and occurs whenever the Floquet multipliers governing the stability of the
limit cycle are complex, with the amplitude of the oscillations increasing as
the instability boundary is approached.
