### 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^{μt}cos(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 | |

State | Published - 1984 |

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### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics

### Cite this

*Mathematical Biosciences*,

*71*(1), 41-55. https://doi.org/10.1016/0025-5564(84)90004-X

**The role of nonreal eigenvalues in the identification of cycles in a compartmental system.** / Eisenfeld, J.; Beltz, W. F.; Grundy, Scott M.

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 71, no. 1, pp. 41-55. https://doi.org/10.1016/0025-5564(84)90004-X

}

TY - JOUR

T1 - The role of nonreal eigenvalues in the identification of cycles in a compartmental system

AU - Eisenfeld, J.

AU - Beltz, W. F.

AU - Grundy, Scott M

PY - 1984

Y1 - 1984

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.

UR - http://www.scopus.com/inward/record.url?scp=48549108359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48549108359&partnerID=8YFLogxK

U2 - 10.1016/0025-5564(84)90004-X

DO - 10.1016/0025-5564(84)90004-X

M3 - Article

VL - 71

SP - 41

EP - 55

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -