In this study, we investigate the oscillatory behavior of the universe within the \(f(R,L_m)\) gravity framework. We propose a model defined by \(f(R,L_m)=\frac{R}{2}+L_m^\alpha \) , where \(\alpha \) is a free parameter, and introduce a phenomenological, time-periodic parametrization of the deceleration parameter to drive cyclic evolution. Our analysis reveals that the universe exhibits smooth and regular oscillations in key cosmological quantities, including the Hubble parameter, deceleration parameter, energy density, pressure, and equation of state (EoS) parameter. Notably, the EoS transitions periodically across the phantom divide, demonstrating a quintom-like dark energy behavior. The model remains physically acceptable, singularity-free, and dynamically stable throughout each cycle. Unlike traditional bouncing cosmologies, our framework achieves cyclic behavior without introducing exotic matter components or a separate bounce mechanism, relying instead on the curvature-matter coupling structure of \(f(R,L_m)\) gravity. Furthermore, the model satisfies key energy conditions within each cycle, reinforcing its physical viability. These results offer a compelling alternative to standard cosmological scenarios and complement recent efforts to describe non-singular cyclic evolution in modified gravity theories.
