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Nonlinear superfluidity and time-delay based chaotic spin-down in pulsars

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.