  Motivated by mirror symmetry, we consider a Lagrangian fibration $X\to B$ and
Lagrangian maps $f:L\hookrightarrow X\to B$, when $L$ has dimension 2,
exhibiting an unstable singularity, and study how their caustic changes, in a
neighbourhood of the unstable singularity, when slightly perturbed. The
integral curves of $\nabla f_x$, for $x\in B$, where $f_x(y)=f(y)-x\cdot y$,
called ``gradient lines'', are then introduced, and a study of them, in order
to analyse their bifurcation locus, is carried out.
