Abstract
We present a low-dimensional truncated model for a viscous fluid contained in a two-dimensional square box, obtained by truncating a dynamical system of amplitudes for the velocity field. This low-dimensional model exhibits a route to chaos via a period doubling cascade (Feigenbaum’s Scenario). In order to compute with high accuracy the period doubling, a numerical method based on the first order variational equations and a Poincaré map has been developed. This methodology can also be applied to the analysis of bifurcations of periodic orbits in low-dimensional ordinary differential equations. This method allows to detect not only the presence of bifurcations but also the computation of stable and unstable periodic orbits. On the other hand, the chaotic dynamics of the system is analyzed in detail by the computation of the Liapunov exponents for long-time integrations. For this purpose, a numerical scheme based on renormalization techniques has been constructed.
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