By means of a self-gravitating gaseous model it has been shown that a globular cluster core makes a non-linear oscillation with an amplitude as large as a factor of 106 in the central density. Core contraction is due to the gravothermal catastrophe. Switching from the contraction to expansion is performed by a small amount of energy input from binary stars. The expansion is driven also by the gravothermal instability but in the opposite direction. Since the oscillation is much slower in stages with lower densities, the probability is much higher of finding post-collapse globular clusters in states with the lower central densities than in the collapsed states with a high-density cusp.
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Sugimoto et al. (1983) studied this question.