  We study a paradigmatic random recurrent neural network introduced by
Sompolinsky, Crisanti, and Sommers (SCS). In the infinite size limit, this
system exhibits a direct transition from a homogeneous rest state to chaotic
behavior, with the Lyapunov exponent gradually increasing from zero. We
generalize the SCS model considering odd saturating nonlinear transfer
functions, beyond the usual choice $\phi(x)=\tanh x$. A discontinuous
transition to chaos occurs whenever the slope of $\phi$ at 0 is a local minimum
(i.e., for $\phi'''(0)>0$). Chaos appears out of the blue, by an
attractor-repeller fold. Accordingly, the Lyapunov exponent stays away from
zero at the birth of chaos.
