  Located at the core of the Galactic Centre, the S-star cluster serves as a
remarkable illustration of chaos in dynamical systems. The long-term chaotic
behaviour of this system can be studied with gravitational $N$-body
simulations. By applying a small perturbation to the initial position of star
S5, we can compare the evolution of this system to its unperturbed evolution.
This results in the two solutions diverging exponentially, defined by the
separation in position space $\delta_{r}$, with an average Lyapunov timescale
of $\sim$420 yr, corresponding to the largest positive Lyapunov exponent. Even
though the general trend of the chaotic evolution is governed in part by the
supermassive black hole Sagittarius $\rm A^{*}$ (Sgr $\rm A^{*}$), individual
differences between the stars can be noted in the behaviour of their
phase-space curves.
  We present an analysis of the individual behaviour of the stars in this
Newtonian chaotic dynamical system. The individuality of their behaviour is
evident from offsets in the position space separation curves of the S-stars and
the black hole. We propose that the offsets originate from the initial orbital
elements of the S-stars, where Sgr $\rm A^{*}$ is considered in one of the
focal points of the Keplerian orbits. Methods were considered to find a
relationship between these elements and the separation in position space.
Symbolic regression turns out to provide the clearest diagnostics for finding
an interpretable expression for the problem. Our symbolic regression model
indicates that $\left\langle\delta_r\right\rangle \propto e^{2.3}$, implying
that the time-averaged individual separation in position space increases
rapidly with the initial eccentricity of the S-stars.
