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A New Approach to Global Stability of Discrete Lotka-Volterra Predator-Prey Models

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  • Young-Hee Kim
  • Sangmok Choo

Abstract

An Euler difference scheme for a three-dimensional predator-prey model is considered and we introduce a new approach to show the global stability of the scheme. For this purpose, we partition the three-dimensional space and calculate the sign of the rate change of population of species in each partitioned region. Our method is independent of dimension and then can be applicable to other dimensional discrete models. Numerical examples are presented to verify the results in this paper.

Suggested Citation

  • Young-Hee Kim & Sangmok Choo, 2015. "A New Approach to Global Stability of Discrete Lotka-Volterra Predator-Prey Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-11, June.
    • Handle: RePEc:hin:jnddns:674027
    DOI: 10.1155/2015/674027
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