2019/12/04 by Leonardo Massai, Massai, Leonardo, Giacomo Como +3
Biochemistry, Genetics and Molecular Biology · #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis
paper · pdf · doi:10.48550/arxiv.1912.01906
openalex publication_date 2019/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study deterministic continuous-time lossy dynamical flow networks with\nconstant exogenous demands, fixed routing, and finite flow and buffer\ncapacities. In the considered model, when the total net flow in a cell\n---consisting of the difference between the total flow directed towards it\nminus the outflow from it--- exceeds a certain capacity constraint, then the\nexceeding part of it leaks out of the system. The ensuing network flow dynamics\nis a linear saturated system with compact state space that we analyze using\ntools from monotone systems and contraction theory. Specifically, we prove that\nthere exists a set of equilibria that is globally asymptotically stable. Such\nequilibrium set reduces to a single globally asymptotically stable equilibrium\nfor generic exogenous demand vectors. Moreover, we show that the critical\nexogenous demand vectors giving rise to non-unique equilibria correspond to\nphase transitions in the asymptotic behavior of the dynamical flow network.\n