  We study the SYK model with complex fermions, in the presence of an
all-to-all $q$-body interaction, with a non-vanishing chemical potential. We
find that, in the large $q$ limit, this model can be solved exactly and the
corresponding Lyapunov exponent can be obtained semi-analytically. The
resulting Lyapunov exponent is a sensitive function of the chemical potential
$\mu$. Even when the coupling $J$, which corresponds to the disorder averaged
values of the all to all fermion interaction, is large, values of $\mu$ which
are exponentially small compared to $J$ lead to suppression of the Lyapunov
exponent.
