CAJ | 학술논문

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-Takens-Newhouse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。
위심입탐토류동적은정성，본문연구료평면불가압축적오모류동계통적동역학행위급방진여공제문제。운용분차도、Lyapunov지수보화방가래절면도분석료계통통과분차과도도혼돈소전현적복잡동역학행위。수치모의게시출해계통가통과Ruelle-Takens-Newhouse도경주향혼돈，토론료계통종규칙운동전화도혼돈운동소구유적보괄특정。설계공제기，병이용연지반궤공제방안，장계통공제도일주기화이주기。
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.