  We investigate the chaotic spin-down behavior seen from some pulsars in terms
of the nonlinear superfluid dynamics. To this end, we numerically solve the set
of equations for the superfluid-normal matter system whose coupling is mediated
by creep of the vortex lines. We show that glitch perturbations which introduce
a time-delay to the steady-state dynamics leave behind a remnant in the third
time derivative of the rotational phase. This time-delay induces a
hyper-chaotic spin-down for pulsars. We find that glitch-induced changes in the
rotational parameters lead to non-closing cyclic patterns in the time-delayed
phase difference diagram. We observe that the number of cycles, $N$, in the
diagram results from $N+1$ glitches occurred in total observation time.
