  The multiscaling properties of the mixed Obukhov-Novikov shell model of
turbulence are investigated numerically and compared with those of the complex
GOY model, mostly studied in the recent years. Two types of generic singular
fluctuations are identified~: first, self-similar solutions propagating from
large to small scales and building up intermittency, second, complex time
singularities inhibiting the cascade and promoting chaos. A simple and robust
method is proposed to track these objects. It is shown that the scaling
exponent of self-similar solutions selected by the dynamics is compatible with
large order statistics whenever it departs enough from the Kolmogorov value.
Complex time singularities on the other hand get trapped on the last shells,
when the proportion of Novikov interactions exceeds a critical value which is
argued to mark the boundary between chaotic and regular dynamics in the limit
of infinite Reynolds number.
