A class of ENSO perturbed model is studied. Using the perturbation theory and method, the asymptotic expansions of solution of corresponding problem are constructed.

We discuss the model of classical risk process perturbed by diffusion in an economic environment, and obtain many calculational formulae on premium according to different premium principles.

To discuss the strictly positive realness judgment criteria of singularly perturbed systems, a singular system model is employed, and the existing positive real lemma of singular systems is improved.