流动系统的混沌行为及仿真与控制  

Chaotic Behavior, Simulation and Control of Flow System

作　　者：崔进[1] 王贺元[1] 

机构地区：[1]辽宁工业大学理学院,锦州121001

出　　处：《工程数学学报》2014年第4期539-544,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(41174090);国家重点基础研究发展973计划(2012CB416605);辽宁省教育厅科研基金(L2013248);锦州市科学技术基金(13A1D32)~~

摘　　要：为深入探讨流动的稳定性,本文研究了平面不可压缩的五模流动系统的动力学行为及仿真与控制问题.运用分岔图、Lyapunov指数谱和庞加莱截面图分析了系统通过分岔过渡到混沌所展现的复杂动力学行为.数值模拟揭示出该系统可通过Ruelle-TakensNewhouse途径走向混沌,讨论了系统从规则运动转化到混沌运动所具有的普适特征.设计控制器,并利用延迟反馈控制方案,将系统控制到一周期和二周期.In order to explore the stability of the flow, we study the nonlinear dynamical behavior, and the simulation and control problem of the five-modes flow system for a two-dimensional incompressible Navier-Stokes equation. Complex dynamical behavior of the system is further explored by calculating its bifurcation diagrams, Lyapunov exponents spectrum and Poincare section. It can be revealed by the numerical simulations that this system can get chaos through Ruelle-Takens-Newhouse route, and the universal features of the system transforming from regularity to chaos are discussed. Designing controller directs the system to a period motion and two period motions by a time-delayed feedback control method.

关 键 词：类LORENZ系统 混沌 分岔 

分 类 号：O175.14[理学—数学] O241.81[理学—基础数学]