Averaging principle for stochastic differential equations in the random periodic regime

We present the validity of stochastic averaging principle for non-autonomous slow–fast differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from multi-scale dynamical systems, where configurations are time dependent due to nonlinearity underlying vector fields and onset invariant sets. Averaging with respect uniform ergodicity motion no longer available in this scenario. The measures on certain minimal Poincaré section used identify limit.