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has been cited by the following article:

• TITLE: A Seven-Dimensional System of the Navier-Stokes Equations for a Two-Dimensional Incompressible Fluid on a Torus

  AUTHORS: Heyuan Wang, Yan Gao

  KEYWORDS: The Navier-Stokes Equations, Strange Attractor, Lyapunov Function, Bifurcation, Chaos

  JOURNAL NAME: Open Journal of Fluid Dynamics, Vol.4 No.4, November 17, 2014

  ABSTRACT: A seven-mode truncation system of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is considered. Its stationary solutions and stability are presented; the existence of the attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through instability of invariant tori, is simulated numerically by computers with the changing of Reynolds number. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, some basic dynamical behaviors of the new chaos system are revealed.