The Role of Nonreal Eigenvalues in the Identification of Cycles in a Compartmental System
Grundy, S. M.
Beltz, W. F.
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The paper concerns the relationship between the cycles in the graph of a compartmental system and the modes of the impulse response function associated with an input-output experiment. Suppose that there is at least one oscillatory mode, [see pdf for notation]. Let [see pdf for notation] be the slowest mode. The main result is that the system contains a cycle of length three or longer and that the length of the longest cycle is at least [see pdf for notation]. The paper also deals with the problem of estimating cycle length from discrete data.