Abstract
We show the quantum correlation between two coupled hybrid optomechanical cavities by quantifying the non-classical correlation using Gaussian quantum discord. This involves analyzing and solving Heisenberg Langevin equations to obtain the (12*12)dimensional covariance matrix of this system. Based on the experimentalist conditions, we simulate quantum correlation of bipartite steady-state with continuous conditions using Guassian quantum discord. We know that the generation of quantum correlation and its robustness essentially depend on the physical parameters of the system. We provide the stability analysis by means of the RuthsHurwitz criterion to confirm the choices made during the analysis of quantum discord dynamics.