Approximating the periodic solutions of the Lotka--Volterra system.

Authors

  • Tatjana Grozdanovski
  • John Shepherd

DOI:

https://doi.org/10.21914/anziamj.v49i0.353

Abstract

The two dimensional Poincare--Lindstedt method is used to obtain approximate solutions to the periodic solutions of the Lotka--Volterra predator-prey system near the non-trivial critical point. These approximations are then used to analyze the behaviour of these solutions and provide a convenient way to describe general solution properties not available from numerical computations. References
  • Grimshaw, R., Nonlinear Ordinary Differential Equations. CRC Press, USA, 1993.
  • Lotka, A. J., Elements of Physical Biology. Williams and Wilkins, Baltimore, Maryland, USA, 1925.
  • Murray, J. D. Mathematical Biology. I. An Introduction. Springer--Verlag, Belin, Heidelberg, 2002.
  • Murty, K. N. and Rao, V. G, Approximate analytical solutions of the general Lotka--Volterra equations, Journal of Mathematical Analysis and Applications, 122, 582--588, 1987.
  • Rothe, F., The periods of the Volterra--Lotka system, J. Reine Angew. Math., 355, 129--138, 1985.
  • Volterra, V. , Variation and Fluctuations of the Number of Individuals in Animal Species Living Together, Translated from 1928 edition by R. N. Chapman, Animal Ecology, Arno, New York, New York, USA, 1931.
  • Waldvogel, J. The period in the Volterra--Lotka predator-prey model, SIAM J. Numer. Anal., 20, 1264--1272, 1983.
  • Waldvogel, J, The period in the Volterra--Lotka system is monotonic, J. Math. Anal. App. l, 114, 178--184, 1986.
  • Willson, A. J, On Varma's prey-predator problem, Bull. Math. Biol., 42, 599--600, 1980.

Published

2008-01-02

Issue

Section

Proceedings Engineering Mathematics and Applications Conference