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We consider stochastic resonance for a diffusion with drift given by apotential, which has two metastable states and two pathways between them.Depending on the direction of the forcing, the height of the two barriers, onefor each path, will either oscillate alternating or in synchronisation. Weconsider a simplified model given by a continuous time Markov Chains with twostates. This was done for alternating and synchronised wells. The invariantmeasures are derived for both cases and shown to be constant for thesynchronised case. A PDF for the escape time from an oscillatory potential isstudied. Methods of detecting stochastic resonance are presented, which arelinear response, signal-noise ratio, energy, out-of-phase measures, relativeentropy and entropy. A new statistical test called the conditionalKolmogorov-Smirnov test is developed, which can be used to analyse stochasticresonance. An explicit two dimensional potential is introduced, the criticalpoint structure derived and the dynamics, the invariant state and escape timestudied numerically. The six measures are unable to detect the stochasticresonance in the case of synchronised saddles. The distribution of escape timeshowever not only shows a clear sign of stochastic resonance, but changing thedirection of the forcing from alternating to synchronised saddles an additionalresonance at double the forcing frequency starts to appear. The conditional KStest reliably detects the stochastic resonance. This paper is mainly based onthe thesis "Stochastic Resonance for a Model with Two Pathways"

A comparative study of stochastic resonance for a model with two  pathways by escape times, linear response, invariant measures and the  conditional Kolmogorov-Smirnov Test