摘要
A five-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented;the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, some basic dynamical behavior of the new chaos system are revealed.
A five-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented;the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, some basic dynamical behavior of the new chaos system are revealed.
作者
Heyuan Wang
Heyuan Wang(College of Sciences, Liaoning University of Technology, Jinzhou, China)
