Two-time-scale stochastic approximation, a generalized version of the popular has found broad applications in many areas including control, optimization, and machine learning. Despite its popularity, theoretical guarantees this method, especially finite-time performance, are mostly achieved for linear case while results nonlinear counterpart very sparse. Motivated by classic control theory sing...

We have suggested that the Yang-Mills(YM) field can be a kind of candidate of inflation at high energy scale or dark energy at the very low energy scale, which can naturally give the matter state of ω < 0, even it can give ω < −1. In this paper, we discuss the perturbation theory of the YM field, and give a series of equations which can describe the evolution of the YM field’s perturbation in t...

The stability, instability, and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point is studied in detail. The critical point is characterized by two distinct pairs of pure imaginary eigenvalues of the Jacobian, and the system is described by two independent parameters. The analysis is based on a generalized perturbation procedure which employs mul...

We consider inhomogeneous preheating in multi-field models of cosmological perturbation. After preheating, two fields are trapped at an enhanced symmetric point. One field is an oscillating field and the other is a light field that plays an important role in generating perturbation. In this presentation, we consider two types of potential for the light field. Submitted for the SUSY07 proceeding...