Sixth Mississippi State Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 67-75.

Nonstandard numerical methods for a class of predator-prey models with predator interference

Dobromir T. Dimitrov, Hristo V. Kojouharov

Abstract:
We analyze a class of predator-prey models with Beddington-DeAngelis type functional response. The models incorporate the mutual interference between predators, which stabilizes predator-prey interactions even when only a linear intrinsic growth rate of the prey population is considered. Positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative features as the corresponding continuous predator-prey models, are formulated and analyzed. The proposed numerical techniques are based on a nonlocal modelling of the growth-rate function and a nonstandard discretization of the time derivative. This approach leads to significant qualitative improvements in the behavior of the numerical solution. Applications of the PESN methods to specific Beddington-DeAngelis predator-prey systems are also presented.

Published February 28, 2007.
Math Subject Classifications: 37M05, 39A11, 65L12, 65L20.
Key Words: Finite-difference; nonstandard; positive; elementary stable; predator-prey; predator interference

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Dobromir T. Dimitrov
Department of Ecology and Evolutionary Biology
University of Tennessee at Knoxville
Knoxville, TN 37996-1610, USA
email: ddimitr1@utk.edu
Hristo V. Kojouharov
Department of Mathematics
University of Texas at Arlington
Arlington, TX 76019-0408, USA
email: hristo@uta.edu

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