Many important processes in a living cell are controlled by DNA, RNA, proteins and dynamic interactions between them. Responding to various external conditions, such as the amount of incident light, presence or absence of nutrients and regulators (a protein complex), the genetic information stored in the DNA is decoded. This process is known as 'transcription', and it produces RNA molecules. The DNA subsequences that have the capability to generate different RNA molecules are called 'genes'. The resulting RNA molecules in turn induce the production of corresponding proteins via a process called 'translation'. Proteins perform many of the biological functions in the cell, which also include the function of 'cell regulation'. As a result, the entire process of transcription and translation can be viewed as 'gene interactions', where the product of one gene controls the activity levels of some others. Identifying the dynamic interaction between various genes would immensely help us understand the associated processes that these genes control. The problem, however, is that these interactions take place at various time scales; the chemical reactions have an inherent randomness and the dynamic equations are often nonlinear. In this paper, we would argue that simple dynamic models can capture dynamic interactions between genes locally in time resulting in a dynamic 'gene regulatory network'. We present a feed forward dynamical systems model, to identify interactions between diurnal genes in Cyanothece sp. ATCC 51142, a unicellular cyanobacterium, under regular day/night cycles and altered light patterns. With the selection of appropriate parameters in the model, we can explain various gene expressions observed in the data. We construct a gene regulatory network and show how the network interconnections change under different 'light conditions'. The model is shown to be sufficient to capture many biologically meaningful interactions between genes including, co-regulation of genes that are located in close proximity in the genome, time delays involved between regulator-target activities, increased level of interactions under transient input conditions, etc. The resultant network consists of various known network motifs. We validate some of the predicted links by showing the presence of common sequences in their corresponding conserved regulatory regions.