Stability and phase transitions of dynamical flow networks with finite capacities
| Autor: | Fabio Fagnani, Leonardo Massai, Giacomo Como |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Equilibrium point
0209 industrial biotechnology 020208 electrical & electronic engineering Mathematical analysis Dynamical flow networks 02 engineering and technology Dynamical Systems (math.DS) Dynamical flow networks nonlinear systems compartmental systems network flows robust control Flow network Stability (probability) compartmental systems Nonlinear system 020901 industrial engineering & automation Monotone polygon Flow (mathematics) Control and Systems Engineering network flows Stability theory 0202 electrical engineering electronic engineering information engineering FOS: Mathematics State space robust control nonlinear systems Mathematics - Dynamical Systems Mathematics |
| DOI: | 10.48550/arxiv.1912.01906 |
| Popis: | We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the difference between the total flow directed towards it minus the outflow from it--- exceeds a certain capacity constraint, then the exceeding part of it leaks out of the system. The ensuing network flow dynamics is a linear saturated system with compact state space that we analyze using tools from monotone systems and contraction theory. Specifically, we prove that there exists a set of equilibria that is globally asymptotically stable. Such equilibrium set reduces to a single globally asymptotically stable equilibrium for generic exogenous demand vectors. Moreover, we show that the critical exogenous demand vectors giving rise to non-unique equilibria correspond to phase transitions in the asymptotic behavior of the dynamical flow network. Comment: 7 pages, 4 figures, submitted at IFAC 2020 |
| Databáze: | OpenAIRE |
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