This thesis investigates the possibility of observing anti-phase oscillation dynamics in biological systems with a limited resource pool, such as ribosomes. The interest lies in understanding how competition for limited resources can drive temporal coordination, optimizing resource utilization and potentially enhancing protein synthesis and cellular growth. The research draws inspiration from two key studies. The first study by Nordick et al. presents a mathematical model, MMI2-SSB, which shows how RNA degradation and noise can generate sustained oscillations in mRNA and miRNA concentrations, even without explicit feedback loops. This demonstrates how post-transcriptional interactions can maintain complex cellular dynamics. The second study by Liu et al.