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Compartmental systems and generating functions

, : Compartmental systems and generating functions. BULL MATH BIOPHYS 27(Spec Issue): 49-63

Compartmental systems can be represented by direct graphs in which each node corresponds to a generating function and each arm to a transfer generating function. A homomorphism is established between a compartmental system and this representation, in analogy with that obtained through the use of the Laplace transformation. From the values obtained experimentally in a given compartment, through the solution of a difference equation, the generating function for the corresponding node can be calculated and the graph of the system can be built up within the degrees of freedom of the model. From the graph it is possible to calculate the transfer generating function between any 2 connected nodes, the mean permanence time in a given node, the mean transit time between 2 nodes, and their precursor-successor order.


DOI: 10.1007/bf02477261

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