Chaos in a discrete model of a two-gene system

We study the complex dynamics of a discrete model of a two-gene system. The discrete time equations of the system are derived from the chemical reactions corresponding to the gene expression and regulation. We show that the system exhibits regular, chaotic and hyper-chaotic behavior, depending on the values taken by the control parameters. The chaotic behavior emerges in systems with increased cooperativity among the transcription factors. Also, we show that synchronization phenomena occurs through a hyper-chaos to chaos transition.