Different ways to turbulence in dissipative dynamical systems

Abstract

The Lorenz model is studied in details for σ = 10, b = 83 and 145 < r < 170. Between r = 145 and r = 148.4 the Lore nz attractor disaggregates itself into a limit cycle through a cascade of bifurcation with successive undoubling of periods. At r = 166.07 this limit cycle looses its stability through "intermittency", giving rise to a second aperiodic attractor. We give a semi-quantitative interpretation of these processes and discuss their relation with the different transitions to turbulence observed experimentally.