### Abstract

A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI.

Original language | English (US) |
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Pages (from-to) | 4233-4250 |

Number of pages | 18 |

Journal | Bulletin of Mathematical Biology |

Volume | 81 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2019 |

### Keywords

- Functional knots
- Oscillatory properties
- PDEs
- Stationary population identity

### ASJC Scopus subject areas

- Neuroscience(all)
- Immunology
- Mathematics(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Environmental Science(all)
- Pharmacology
- Agricultural and Biological Sciences(all)
- Computational Theory and Mathematics

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## Cite this

*Bulletin of Mathematical Biology*,

*81*(10), 4233-4250. https://doi.org/10.1007/s11538-019-00652-7