Nonstandard Numerical Methods for a Class of Predator-prey Models with Predator Interference
نویسندگان
چکیده
We analyze a class of predator-prey models with BeddingtonDeAngelis 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 predatorprey 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.
منابع مشابه
Nonstandard finite-difference methods for predator-prey models with general functional response
Predator-prey systems with linear and logistic intrinsic growth rate of the prey are analyzed. The models incorporate the mutual interference between predators into the functional response which stabilizes predatorprey interactions in the system. Positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative features as the corresponding continuous pred...
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