Life on earth is strongly regulated by the daynight cycle, widely known as diurnal cycle. Accordingly, many organisms have developed an internal time keeping mechanism; circadian clock, in order to maintain these rhythms even with short term modification of the external light patterns. In previous studies, different biological processes have been identified as either diurnal or circadian controlled. In order to understand the interactions between these processes and the effect of external light input on the individual rhythms, it is important to develop a mathematical model which can capture the essential dynamics of these rhythms. In this work, we propose a simple interacting oscillatory network model, which is sufficient to capture the different behavioral patterns in the biological processes. We show that this model is capable of reproducing the actual gene behaviors observed under different light input patterns. Also, the model proposed is shown to be resilient to noise. We use the model to understand the synchronization between different processes; the modulation of internal clock by the external light input; the changes expected in circadian clock and other peripheral processes under different light patterns, etc. We relate some of the simulation results with already available biological knowledge. We discuss effects of different network topologies which can be investigated by the future experiments.