  We study the oscillatory dynamics in the generic three-species
rock-paper-scissors games with mutations. In the mean-field limit, different
behaviors are found: (a) for high mutation rate, there is a stable interior
fixed point with coexistence of all species; (b) for low mutation rates, there
is a region of the parameter space characterized by a limit cycle resulting
from a Hopf bifurcation; (c) in the absence of mutations, there is a region
where heteroclinic cycles yield oscillations of large amplitude (not robust
against noise). After a discussion on the main properties of the mean-field
dynamics, we investigate the stochastic version of the model within an
individual-based formulation. Demographic fluctuations are therefore naturally
accounted and their effects are studied using a diffusion theory complemented
by numerical simulations. It is thus shown that persistent erratic oscillations
(quasi-cycles) of large amplitude emerge from a noise-induced resonance
phenomenon. We also analytically and numerically compute the average escape
time necessary to reach a (quasi-)cycle on which the system oscillates at a
given amplitude.
