Understanding stochastic resonance and hysteresis in climate considering state-dependent fluctuations

We consider two aspects in climatic science where bistability between the two stable states of the systems is observed. One is the transition between the glacial and the interglacial phase in Earth's glacial cycle. Another is the thermohaline circulation in the North Atlantic ocean. It is possible to model both of these phenomena by the overdamped dynamics of a Brownian particle in a double-well potential subject to periodic forcing. For the former, the two wells correspond to two different climates and the periodic forcing is sufficiently weak so that no transition can occur between the two states without noise. Whereas in case of the latter, the two states represent two different conditions of the flow and the strength of the periodic forcing is high enough to cause hysteresis in the system. We suggest that the short-term fluctuations related to weather, in both of these two cases, depend on the present climatic state of the system. This leads to the introduction of the state-dependent diffusion coefficients in the dynamics because the diffusion coefficient takes into account the strength of the fluctuations. We show that this consideration produces important features in the dynamics which agree with the real observations for both the glacial cycles and thermohaline flow.