Journal of Mathematical Biology

, Volume 27, Issue 5, pp 491–506

A nonautonomous model of population growth

  • R. R. Vance
  • E. A. Coddington


With x = population size, the nonautonomous equation x = xf(t,x) provides a very general description of population growth in which any of the many factors that influence the growth rate may vary through time. If there is some fixed length of time (usually long) such that during any interval of this length the population experiences environmental variability representative of the variation that occurs in all time, then definite conclusions about the population's long-term behavior apply. Specifically, conditions that produce population persistence can be distinguished from conditions that cause extinction, and the difference between any pair of solutions eventually converges to zero. These attributes resemble corresponding features of the related autonomous population growth model x = xf(x).

Key words

Environmental variation Nonautonomous Population growth 


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • R. R. Vance
    • 1
  • E. A. Coddington
    • 2
  1. 1.Department of BiologyUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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