On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations

Arni S.R.Srinivasa Rao, James R. Carey

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 languageEnglish (US)
Pages (from-to)4233-4250
Number of pages18
JournalBulletin of Mathematical Biology
Issue number10
StatePublished - Oct 1 2019


  • 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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