报告题目：Modelling and analysis of dynamics for a 3D  mixed Lorenz system with a damped term
 
报告人：李先义 教授 （扬州大学）
 
报告时间：2015年11月30日（星期一）下午 3：30 - 4：30
报告地点：数学楼二楼学术报告厅



 
摘要：The work in this paper consists of two parts. The one is modelling. After a method of classification for three dimensional (3D) autonomous chaotic systems and a concept of mixed Lorenz system are introduced, a mixed Lorenz system with a damped term is presented. 
 The other is the analysis for dynamical properties of this model. First, its local stability and bifurcation in its parameter space are in detail considered. Then, the existence of its homoclinic and heteroclinic orbits, and the existence of singularly degenerate heteroclinic cycles, are studied by rigorous theoretical analysis. 
 Finally, by using the Poincare compactification for polynomial vector fields in R^3, a global analysis of this system near and at infinity is presented, including the complete description of its dynamics on the sphere near and at infinity.
 Simulations corroborate corresponding theoretical results. In particular, a possibly new mechanism behind the creation of chaotic attractors, consisting of the change for the dimensional number of stable manifold of the saddle at the origin as the parameter b crosses the null value, is proposed.
 Based on the knowledge of this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b>0.