Introduction and Mathematical Preliminaries

  • Fred Brauer
  • Carlos Castillo-Chávez
Part of the Texts in Applied Mathematics book series (TAM, volume 40)


In the 1920s Vito Volterra was asked if it were possible to explain the fluctuations which had been observed in the fish population of the Adriatic sea—fluctuations which were of great concern to fishermen in times of low fish populations. Volterra (1926) constructed the model which 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 New York 2001

Authors and Affiliations

  • Fred Brauer
    • 1
  • Carlos Castillo-Chávez
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Dept. of Theoretical and Applied MechanicsMathematical and Theoretical Biology InstituteUSA
  3. 3.Biometrics DepartmentCornell UniversityIthacaUSA

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