Introduction and Mathematical Preliminaries

Part of the Texts in Applied Mathematics book series (TAM, volume 40)


In the 1920’s Vito Volterra was asked whether it would be possible to explain the fluctuations that had been observed in the fish population of the Adriatic sea–fluctuations that were of great concern to fishermen in times of low fish populations. Volterra (1926) constructed the model that has become known as the Lotka-Volterra model (because A.J. Lotka (1925) constructed a similar model in a different context about the same time), based on the assumptions that fish and sharks were in a predator–prey relationship.


Periodic Solution Periodic Orbit Equilibrium Point Saddle Point Phase Portrait 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Mathematical and Computational Modeling Sciences Center (MCMSC)Arizona State UniversityTempeUSA

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