A Theory of Stochastic Resonance in Climatic Change

In this paper we study a one-dimensional, nonlinear stochastic differential equation when small amplitude, long-period forcing is applied. The equation arises in the theory of the climate of the earth. We find that the cooperative effect of the stochastic perturbation and periodic forcing lead to an amplification of the peak of the power spectrum, due to a mechanism that we call stochastic resonance. A heuristic analysis of the resonance condition is presented and our analytical findings are confirmed by numerical calculations.