  The aim of this paper is to investigate the stable/unstable regimes of the
non-static anisotropic filamentary stellar models in the framework of
$f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity. We construct the field equations and
conservation laws in the perspective of this gravity. The perturbation scheme
is applied to analyze the behavior of a particular
$f(R,T,R_{\mu\nu}T^{\mu\nu})$ cosmological model on the evolution of
cylindrical system. The role of adiabatic index is also checked in the
formulations of instability regions. We have explored the instability
constraints at Newtonian and post-Newtonian limits. Our results reinforce the
significance of adiabatic index and dark source terms in the stability analysis
of celestial objects in modified gravity.
