Context : Core collapse is a prominent evolutionary stage of self-gravitating systems .
In an idealised collisionless approximation , the region around the cluster core evolves in a self-similar way prior to the core collapse .
Thus , its radial density profile outside the core can be described by a power law , \rho \propto r ^ { - \alpha } .

Aims : We aim to find the characteristics of core collapse in N -body models .
In such systems , a complete collapse is prevented by transferring the binding energy of the cluster to binary stars .
The contraction is , therefore , more difficult to identify .

Methods : We developed a method that identifies the core collapse in N -body models of star clusters based on the assumption of their homologous evolution .

Results : We analysed different models ( equal- and multi-mass ) , most of which exhibit patterns of homologous evolution , yet with significantly different values of \alpha : the equal-mass models have \alpha \approx 2.3 , which agrees with theoretical expectations , the multi-mass models have \alpha \approx 1.5 ( yet with larger uncertainty ) .
Furthermore , most models usually show sequences of separated homologous collapses with similar properties .
Finally , we investigated a correlation between the time of core collapse and the time of formation of the first hard binary star .
The binding energy of such a binary usually depends on the depth of the collapse in which it forms , for example from 100 kT to 10 ^ { 4 } kT in the smallest equal-mass to the largest multi-mass model , respectively .
However , not all major hardenings of binaries happened during the core collapse .
In the multi-mass models , we see large transfers of binding energy of \sim 10 ^ { 4 } kT to binaries that occur on the crossing timescale and outside of the periods of the homologous collapses .

Conclusions :