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A note on exact solutions of two prey-predator equations

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Abstract

Exact solutions are obtained and discussed for classes of Lotka-Volterra and Leslie-Gower systems governing the interaction of two species. The classes are defined by certain constraints which are imposed on the time-dependent parameters of the equations. A general result for such systems is that each species is characterised by two time-scales: one representing natural growth and the other, the interdependence of the species.

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Literature

  • Abramowitz, M. and I. A. Stegun. 1965.Handbook of Mathematical Functions. New York: Dover Publications Inc.

    Google Scholar 

  • Leslie, P. H. and J. C. Gower. 1960. “The Properties of a Stochastic Model for the Predator-Prey Type of Interaction Between Two Species.”Biometrika 47, 219–234.

    Article  MATH  MathSciNet  Google Scholar 

  • Pielou, E. C. 1969.An Introduction to Mathematical Ecology. New York: Wiley-Interscience.

    MATH  Google Scholar 

  • Rosen, R. 1978. “Dynamical Similarity and the Theory of Biological Transformations.” Bull. math. Biol.40, 549–579.

    MATH  MathSciNet  Google Scholar 

  • Varma, V. S. 1977. “Exact Solutions for a Special Prey-Predator or Competing Species System.”Bull. math. Biol. 39, 619–622.

    MathSciNet  Google Scholar 

  • Willson, A. J. 1980. “On Varma's Prey-Predator Problem.”Bull. math. Biol. 42, 599–600.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computing, Paisley College of Technology, High Street, PA1 2BE, Paisley, Scotland

    R. R. Burnside

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  1. R. R. Burnside
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Burnside, R.R. A note on exact solutions of two prey-predator equations. Bltn Mathcal Biology 44, 893–897 (1982). https://doi.org/10.1007/BF02465187

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  • DOI: https://doi.org/10.1007/BF02465187

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