Stochastic resonance for two competing species in the presence of colored noise

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.