This paper explores the dynamics of evolving cluster of stars in the presences of exotic matter. The $f\left(R\right)$ theory is used to presume exotic terms for evolution scenario. We use structure scalars as evolution parameters to explore dynamics of spherically symmetric distribution of evolving cluster of stars. We consider Starobinsky model, $f\left(R\right)=R+ϵR^2$ and study different evolution modes having features like isotropic pressure, density homogeneity, homologous and geodesic behavior. It is concluded that dynamics of these modes of evolution depends upon the behavior of dark matter. The presences of dark matter directly affects the features of cluster like anisotropic pressure, dissipation, expansion, shear as well as density homogeneity. The evolution having homogeneous density and isotropic pressure depends upon conformally flat and non-dissipative behavior of baryonic as well as non baryonic matter. The dissipation factor induces density inhomogeneity in the expanding clusters having shear effects. The non dissipative homologous evolution also be discussed in the presence and absence of shear effects. It is found that high curvature geometry in the presence of shear supports homologous evolution. Expanding clusters are also explored in the presences of dissipation of dark matter and shear effects. By using quasi-homologous conditions the geodesic evolution is studied. It is theoretically showed that geodesic and homologous conditions depends upon each other. Finally we investigate behavior of Starobinsky model for a stellar structure $4U1820-30$ toward center. It is found that for increasing values of $ϵ$ the DM behavior is dominant as compare to baryonic matter.

本文探讨了在奇异物质存在的情况下演化星团的动力学。这$F\left(\mathrm{电阻}\right)$理论用于假设进化场景的奇异术语。我们使用结构标量作为演化参数来探索演化星团球对称分布的动力学。我们考虑 Starobinsky 模型，$F\left(\mathrm{电阻}\right)=\mathrm{电阻}+\epsilon {\mathrm{电阻}}^2$并研究具有各向同性压力、密度均匀性、同源性和测地线行为等特征的不同演化模式。得出的结论是，这些进化模式的动力学取决于暗物质的行为。暗物质的存在直接影响星团的各向异性压力、耗散、膨胀、剪切以及密度均匀性等特征。具有均匀密度和各向同性压力的演化取决于重子和非重子物质的共形平坦和非耗散行为。耗散因子在具有剪切效应的扩展簇中引起密度不均匀。在存在和不存在剪切效应的情况下也讨论了非耗散同源演化。发现存在剪切的高曲率几何支持同源演化。在暗物质耗散和剪切效应存在的情况下，也探索了扩展的星团。通过使用准同源条件研究测地线演化。理论上表明，测地线和同源条件相互依赖。最后，我们研究了恒星结构的 Starobinsky 模型的行为$4你1820-30$向中心。发现对于增加的值$\epsilon$ 与重子物质相比，DM 行为占主导地位。