Structural polyhedral stability of a biochemical network is equivalent to finiteness of the associated generalised Petri net
Franco Blanchini,
Carlos Andrés Devia,
Giulia Giordano
Abstract:We consider biochemical systems associated with a generalised class of Petri nets with possibly negative token numbers. We show that the existence of a structural polyhedral Lyapunov function for the biochemical system is equivalent to the boundedness of the associated Petri net evolution or, equivalently, to the finiteness of the number of states reachable from each initial condition. For networks that do not admit a polyhedral Lyapunov function, we investigate whether it is possible to enforce polyhedral str… Show more
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