We study a seven dimensional nonlinear dynamical system obtained by a truncation of the Navier–Stokes equations for a two dimensional incompressible fluid with the addition of a linear term modelling the drag friction. We show the bifurcation sequence leading from laminar steady states to chaotic solutions with increasing Reynolds number. Finally, we design an adaptive control which drives the state of the system to the equilibrium point representing the stationary solution.
Gambino, G., Lombardo, M.C., Sammartino, M. (2009). Adaptive control of a seven mode truncation of the Kolmogorov flow with drag. CHAOS, SOLITONS AND FRACTALS, 2009, 47-59 [10.1016/j.chaos.2007.11.003].
Adaptive control of a seven mode truncation of the Kolmogorov flow with drag
GAMBINO, Gaetana;LOMBARDO, Maria Carmela;SAMMARTINO, Marco Maria Luigi
2009-01-01
Abstract
We study a seven dimensional nonlinear dynamical system obtained by a truncation of the Navier–Stokes equations for a two dimensional incompressible fluid with the addition of a linear term modelling the drag friction. We show the bifurcation sequence leading from laminar steady states to chaotic solutions with increasing Reynolds number. Finally, we design an adaptive control which drives the state of the system to the equilibrium point representing the stationary solution.
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