Evolution of cluster of stars in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e243" altimg="si6.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> gravity

This paper explores the dynamics of evolving cluster stars in presences exotic matter. The $f(R)$ theory is used to presume terms for evolution scenario. We use structure scalars as parameters explore spherically symmetric distribution stars. consider Starobinsky model, $f(R)=R+\epsilon R^2$ and study different modes having features like isotropic pressure, density homogeneity, homologous geodesic behavior. It concluded that these depends upon behavior dark matter directly affects anisotropic dissipation, expansion, shear well homogeneity. homogeneous pressure conformally flat non-dissipative baryonic non dissipation factor induces inhomogeneity expanding clusters effects. dissipative also be discussed presence absence found high curvature geometry supports evolution. Expanding are explored By using quasi-homologous conditions studied. theoretically showed each other. Finally we investigate model a stellar $4U 1820-30$ toward center. increasing values $\epsilon$ DM dominant compare