  We study a shell model for the energy cascade in three dimensional turbulence
at varying the coefficients of the non-linear terms in such a way that the
fundamental symmetries of Navier-Stokes are conserved. When a control parameter
$\epsilon$ related to the strength of backward energy transfer is enough small,
the dynamical system has a stable fixed point corresponding to the Kolmogorov
scaling. This point becomes unstable at $\epsilon=0.3843...$ where a stable
limit cycle appears via a Hopf bifurcation. By using the bi-orthogonal
decomposition, the transition to chaos is shown to follow the Ruelle-Takens
scenario. For $\epsilon > 0.3953..$ the dynamical evolution is intermittent
with a positive Lyapunov exponent. In this regime, there exists a strange
attractor which remains close to the Kolmogorov (now unstable) fixed point, and
a local scaling invariance which can be described via a intermittent
one-dimensional map.
