The circuit-breaking algorithm for monotone systems.
In earlier work, we have introduced the circuit-breaking algorithm (CBA) for the analysis of intracellular regulation networks. This algorithm uses the network topology to construct a one-dimensional circuit-characteristic whose zeros correspond to the fixed points of the system. In this study, we apply the CBA to monotone systems whose flow preserves a partial order with respect to some orthant cone. We consider relations between stability of fixed points and the derivative of the corresponding zeros of the circuit-characteristic. In particular, we derive sufficient conditions for instability in case of global asymptotic stability of the open-loop system. Furthermore, we fully characterize stability of the fixed points if in addition the system is monotone. Combined with the theory of monotone systems, our results are used to characterize the long-term behavior of two models for different intracellular regulation processes.
Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany.
Caterina
C
Thomaseth
Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany.
Karsten
K
Kuritz
Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany.
Frank
F
Allgöwer
Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany. Electronic address: Nicole.Radde@ist.uni-stuttgart.de.
Nicole
N
Radde
D000465:Algorithms; D006801:Humans; D020935:MAP Kinase Signaling System; D008962:Models, Theoretical
Circuit-breaking algorithm; Input/output characteristic; MAPK signaling pathway; Monotone system