Coupling and synchronization of piecewise linear genetic regulatory systems

Biological regulatory networks are composed of smaller basic motifs. Some of the most frequent motifs are known as the positive and negative feedback loops, whose individual dynamics is well characterized. This work studies the coupling of two or more identical basic motifs, under diffusive coupling, and analyses their capacity for synchronization and other dynamical properties, such as the generation of new steady states. The feedback loops are described by piecewise linear differential equations, a formalism which allows for further mathematical analysis results.