Multistability, oscillations and bifurcations in feedback loops - Maria Conceição A. Leite; Yunjiao Wang (Mathematical Biosciences and Engineering)
Feedback loops are found to be important network structures inregulatory networks of biological signaling systems because they areresponsible for maintaining normal cellular activity. Recently,the functions of feedback loops have received extensive attention.The existing results in the literature mainly focus on verifyingthat negative feedback loops are responsible for oscillations,positive feedback loops for multistability, and coupled feedbackloops for the combined dynamics observed in their individual loops.In this work, we develop a general framework for studying systematicallyfunctions of feedback loops networks. We investigate the generaldynamics of all networks with one to three nodes and one to two feedback loops. Interestingly, our results are consistent with Thomas' conjectures although we assume each node in the network undergoes a decay, which corresponds to a negative loop in Thomas' setting. Besides studying how network structures influence dynamics at the linear level, we explore thepossibility of network structures having impact on the nonlineardynamical behavior by using Lyapunov-Schmidt reduction and singularity theory.