  Transition to hyperchaotic regimes in Rayleigh-Benard convection in a square
periodicity cell is studied by three-dimensional numerical simulations. By
fixing the Prandtl number at P=0.3 and varying the Rayleigh number as a control
parameter, a bifurcation diagram is constructed where a route to hyperchaos
involving quasiperiodic regimes with two and three incommensurate frequencies,
multistability, chaotic intermittent attractors and a sequence of boundary and
interior crises is shown. The three largest Lyapunov exponents exhibit a linear
scaling with the Rayleigh number and are positive in the final hyperchaotic
attractor. Thus, a route to weak turbulence is found.
