Coupled feedback loops form birhythmicity and inhomogeneous limit cycles of synthetic regulatory networks

Networks composed of complicated interconnections among components could exhibit complicated dynamic behaviors. Some subnetworks are often identified as network motifs for their particular functioning. Among those network motifs, feedback loops play important dynamical roles. Here we show that the coupled feedback loops could show abundant dynamic behaviors, such as birhythmicity and inhomogeneous limit cycle. We investigate the dynamical role of each coupled structure by means of bifurcation diagrams. Through varying one parameter value, we analyze the occurrence of birhythmicity and inhomogeneous limit cycles and locate the different domains of complex oscillatory behaviors in parameter intervals.