Journal of Mathematical Biology
, Volume 27, Issue 5, pp 491506
First online:
A nonautonomous model of population growth
 R. R. VanceAffiliated withDepartment of Biology, University of California
 , E. A. CoddingtonAffiliated withDepartment of Mathematics, University of California
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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 longterm 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 Title
 A nonautonomous model of population growth
 Journal

Journal of Mathematical Biology
Volume 27, Issue 5 , pp 491506
 Cover Date
 198909
 DOI
 10.1007/BF00288430
 Print ISSN
 03036812
 Online ISSN
 14321416
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Environmental variation
 Nonautonomous
 Population growth
 Authors

 R. R. Vance ^{(1)}
 E. A. Coddington ^{(2)}
 Author Affiliations

 1. Department of Biology, University of California, 90024, Los Angeles, CA, USA
 2. Department of Mathematics, University of California, 90024, Los Angeles, CA, USA