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Dynamics in numerics: On a discrete predator-prey model

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Abstract

In this paper, we consider the dynamics of a discrete predator-prey model which is a result of discretization of the corresponding continuous Lotka-Volterra predator-prey model. Among the topis are equilibria and their stability, existence and stability of a period-2 orbit, as well the chaotic behavior of F. The chaos here is in the sense of topological horseshoe and is obtained for certain range of parameter values by applying a recent result from [5]. Our results are in contrast to the recent ones in [6] which claimed that if the predator-prey interaction is replaced by cooperative or competitive interaction, the discretization preserves the property of convergence to the equilibrium, regardless of the step size.

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Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, Guangzhou, 510275, P. R. China

    Yu Huang

  2. Department of Computer and Mathematical Sciences, University of Toronto at Scarborough, Toronto, Ontario, Canada, M1C 1A4

    Xiamei Jiang

  3. Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada, N6A 5B7

    Xingfu Zou

Authors
  1. Yu Huang
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  2. Xiamei Jiang
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  3. Xingfu Zou
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Corresponding author

Correspondence to Yu Huang.

Additional information

Supported in part by NSF of China (10771222), NSF of Guangdong Province, by NSERC of Canada, by MITACS-NCE of Canada and by the Premier Research Excellence Award Program of Ontario.

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Huang, Y., Jiang, X. & Zou, X. Dynamics in numerics: On a discrete predator-prey model. Differ Equ Dyn Syst 16, 163–182 (2008). https://doi.org/10.1007/s12591-008-0010-6

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  • DOI: https://doi.org/10.1007/s12591-008-0010-6

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