The role of nonreal eigenvalues in the identification of cycles in a compartmental system

J. Eisenfeld, W. F. Beltz, Scott M Grundy

Research output: Contribution to journalArticle

6 Scopus citations


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, eμtcos(vt - α). Let eρ{variant}t be the slowest mode. The main result is that the system contains a cycle of length 3 or longer and that the length of the longest cycle is at least π/tan-1[|v|/(ρ{variant}-μ)]. The paper also deals with the problem of estimating the cycle length from discrete data.

Original languageEnglish (US)
Pages (from-to)41-55
Number of pages15
JournalMathematical Biosciences
Issue number1
StatePublished - Sep 1984


ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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