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Mathematics and Recurrent Population Outbreaks

  • Torsten LindströmEmail author
Living reference work entry

Abstract

Despite that outbreaks had been observed for hundreds of years for many populations, it took until the 1920s before the first mechanisms that did not involve human interference were suggested. Just a few mechanisms were included in the first models and the question whether the inclusion of other, very plausible, mechanisms could alter the predictions remained.

In this chapter, we follow the development of models that have been proposed to explain oscillatory population dynamics from the early models suggested by Lotka (1925) and Volterra (1926) until global dynamical questions that are still open for models incorporating explicit resource dynamics, like the chemostat, cf Kuang (1989).

Keywords

Global stability Limit cycle Lyapunov function Mechanistic population models Oscillatory dynamics Recurrent outbreaks 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsLinnaeus UniversityVäxjöSweden

Section editors and affiliations

  • Torsten Lindström
    • 1
  • Bharath Sriraman
    • 2
  1. 1.Linneaeus UniversityVäxjöSweden
  2. 2.Department of Mathematical SciencesThe University of MontanaMissoulaUSA

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