0000000001336117
AUTHOR
Gambino, Gaetana
showing 2 related works from this author
Analysis and control of a seven mode truncation of the Kolmogorov flow with drag.
2008
The transition from laminar to chaotic motion in a viscous fluid flow is investigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov flow with drag friction. Analytical expressions of the bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynoplds number is increased for fixed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is obtained through a model reference approach which makes the control global.
Pattern formation driven by cross-diffusion
2009
In this work we are interested in describing the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms (which take into account the self and the cross-diffusion effects). The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The cross-diffusion is proved to be the key mechanism of pattern formation via a linear stability analysis. A weakly nonlinear multiple scales analysis is carried out to predict the amplitude and the form of the pattern close to the bifurcation threshold. In particular, the Stuart-Landau equation which rules the evolution of the amplitude of the most unstable mode is found. In the subcritica…