Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 15 (2007), pp. 67-75. 

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

Authors: Dobromir T. Dimitrov (Univ. of Tennessee, Knoxville, TN, USA)
         Hristo V. Kojouharov (Univ. of Texas, Arlington, TX, USA)
 
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