Theory of stochastic resonance with state-dependent diffusion

Several interesting and important natural processes are the manifestation of the interplay of nonlinearity and fluctuations. Stochastic resonance is one such mechanism and is crucial to explain many physical, chemical, and biological processes, as well as having huge technological importance. The general setup to describe stochastic resonance considers two states. Recently, it has been unveiled that it is necessary to consider the intrinsic fluctuations related to the two different states of the system are different in interpreting certain fundamental natural processes, such as glacial-interglacial transitions in Earth's ice age. This also has significance in developing advantageous technologies. However, until now, there has been no general theory describing stochastic resonance in terms of the transition rate between the two states and their probability distribution function while considering different noise amplitudes or fluctuation characteristics of these two states. The development of this fundamental theory is attempted in the present research work. As a first step, a relevant approximation is used in which the system is considered within the adiabatic limit. The analytical derivations are corroborated by numerical simulation results. Furthermore, a semianalytical theory is proposed for the definite system without any approximations as the exact analytical solution is not achievable. This semianalytical theory is found to replicate the results obtained from the Brownian dynamics simulation study for previously known quantifiers for stochastic resonance which are estimated in the present context for the system with state-dependent diffusion.