Obukhov and Novikov interactions. Our goal here is to provide the reader with data and facts, disentangled from any theoretical interpretation. An attempt of comparison with the GOY model is made. Section 4 is devoted to the hunt for self-similar solutions and a confrontation of their scaling properties with the statistics of the model at large orders. Complex time singularities are introduced and studied in Section 5, while perspectives and conclusions are briefly outlined in Section 6.

General properties of the model
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Definitions and basic considerations
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As already said in the Introduction, scalar shell models define a velocity variable $u_{n}$, real or complex, on a one-dimensional array of wave-vectors $k_{n}=k_{0}Q^{n}$ where the integer $n$ runs from $0$ to $N$. In most of the paper we shall restrict ourselves to the case of real variables. It simplifies notations to consider that the $u_{n}$ form a ($N+1$)-dimensional vector $\vec u$. The equation of motion then takes the following form $$\frac{d}{dt}\vec{u} =\vec{N}[\vec{u}]+\vec{F}-\vec{D}
\label{equmod1}$$ where the three vectors $\vec N$, $\vec F$, $\vec D$ embody respectively the non-linearities, the external forcing and the dissipation. We only considered a deterministic forcing acting on the $\mbox{zero}^{th}$ shell and usual viscous dissipation, which means $$F_{n}=f\delta 