  We study the role of multiplicative colored noise for different values of the
correlation time $\tau_c$ in the dynamics of two competing species, described
by generalized Lotka-Volterra equations. The multiplicative colored noise
models the interaction between the species and the environment. The interaction
parameter between the species is a random process which obeys a stochastic
differential equation with a generalized bistable potential in the presence of
a periodic driving term, which accounts for the environment temperature
variation. The bistable potential is useful to describe the coexistence and
exclusion dynamical regimes of the ecosystem. Noise-induced periodic
oscillations of the species concentrations and stochastic resonance phenomenon
appear due to the presence of the multiplicative noise. We find that for low
values of the correlation time $\tau_c$ the response of the system coincides
with that obtained with multiplicative white noise. For higher values of
$\tau_c$ the coherent response of the system and the maximum of the
signal-to-noise ratio, signature of the stochastic resonance phenomenon, are
shifted towards higher values of the noise intensity.
