  Based on the Melnikov method, we investigate chaotic behaviors in the
extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole
under temporal and spatial perturbations. Our results show that the temporal
perturbation coming from a thermal quench of the spinodal region in the phase
diagram may cause the temporal chaos only when the perturbation amplitude is
above a critical value, which involves the angular momentum . Under the spatial
perturbation, however, it is found that the spatial chaos always occurs, which
is independent of the perturbation amplitude.
