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

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

doi:10.1016/0025-5564(84)90004-X

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

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

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6 Scopus citations

Abstract

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, e^μtcos(vt - α). Let e^ρ{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 language	English (US)
Pages (from-to)	41-55
Number of pages	15
Journal	Mathematical Biosciences
Volume	71
Issue number	1
DOIs	https://doi.org/10.1016/0025-5564(84)90004-X
State	Published - 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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10.1016/0025-5564(84)90004-X

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abstract = "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.",

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AU - Beltz, W. F.

AU - Grundy, Scott M

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N2 - 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.

AB - 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.

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

Abstract

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