# 关于国防科技大学黄建华教授、玉林师范学院刘永建教授来校讲学的通知

In this talk, we present some results about for the Kordeweg-de Vries equation. Firstly, we prove the analytic radius does not decay faster than $t^{-\frac{1}{4}} as time$t$goes to infinity. Then we present some new idea to prove the Chuehov-Lasicha quasi-stable estimates for the KdV equation on$R$. the global attractor has a finite fractal dimension in the sharp space$H^3(R)$whenever the force belongs to$L^2(R)\$. For the high-order damped stochastic kdv equations with Brownian motion and Poisson jump processes, we prove the existence of the invariant measure, which is ergodic. This is a joint work with Ming Wang and Pengfei Xu.

Based on the KCC geometric invariants, three types of static bifurcations in 2D differential systems, i.e., saddle-node bifurcation, transcritical bifurcation, and pitchfork bifurcation, are discussed in this paper. The dynamics far from fixed points of the systems generating bifurcations are characterized by the deviation curvature and nonlinear connection. In the nonequilibrium region, nonlinear stability of systems is not simple but involves alternation between stability and instability, even though systems are invariably Jacobi-unstable. The results also indicate that the dynamics in the nonequilibrium region are node-like for three typical static bifurcations.