We show analytically that a collective action of two correlated Gaussian white noises, a constant external forcing and a periodic signal leads to a linear stochastic resonance (LSR). The resonance persists for long times, survives averaging over the initial phase of the signal and is characterized by a clear maximum of the signal-to-noise ratio (SNR), unlike other cases of the LSR reported previously. We show that the problem of the LSR is closely related to the behavior of a generalized noisy logistic equation.

PACS numbers: 05.40.Ca, 87.23.Cc