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We developed a mathematical model to derive time scales and the presence ofBS stars. The model is based on the variation of mass through a circle into thecluster defined by a radius, and at a time; this mass cross is translated intoa differential equation that it can be integrated for a given radius (r) and adetermined time (t). From this equation we can derive the different time scalesthat allows us to reach conclusions like: clusters not containing bluestrugglers (BS) stars disappear younger than those clusters containing BS. Inclusters containing BS stars, the volume which takes up half of the clustermass is bigger than the one corresponding to clusters without BS stars but thetime to catch it up is shorter. We also studied, by means of this equation, thecore collapse of stars of the cluster and the region where this concentrationis stopped/retained; this region is identified by means of the relation $c/ch$,being $c=\log(rt/rc)$ and $ch=\log(rc/rh)$. Where rt and rc are the tidal andthe core radius respectively, and rh is the radius where half of the clustermass is concentrated. The model also drove us to the conclusion that the numberof the blue straggler stars in a cluster follows a distribution function whosecomponents are the ratio between relaxation time and the age, labelled as $\itf$, and a factor, named $\varpi$, which is an indicator of the origin of theBS; $\varpi$ increases as the number of BS increase but it is limitedto$\sim$5.0. The mentioned distribution function is expressed as $\it NBS$$\sim$ $\it f^3$($\frac{1}{e^{\frac{f}{\varpi}}-1}$). The validity of thisfunction was carried out by means of matching the number of observed bluestraggler (BS) stars to the number of predicted ones in the available sample ofOC.

Open clusters: time-scales, core collapse and blue stragglers