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1997年国际大学生数学建模竞赛a题获奖论文.pdf

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1997年国际大学生数学建模竞赛a题获奖论文.pdf

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1997年国际大学生数学建模竞赛a题获奖论文.pdf

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文档介绍:Gone Huntin’ 243
Gone Huntin’: Modeling Optimal
Predator and Prey Strategies
Hei (Celia) Chan
Robert A. Moody
David Young
Pomona College
Claremont, CA 91711
Advisor: Richard Elderkin
Summary
We develop a model for the hunting strategy of Velociraptor mongoliensis
pursuing Thescelosaurus neglectus. Regarding their characteristics, there are
discrepancies between the problem statement and the literature; so we para-
meterize our model in terms of both physical and mechanical characteristics.
The primary locomotive differences between the animals are their relative
speeds and turning radii. We show that the optimal strategies are simple, and
we present equations and illustrations for the key components of the model.
Since the optimal strategy for the predator includes a stochastic component,
we present an equation for the probability of a successful encounter.
We also model the interaction of multiple predators and multiple prey. With
a reasonable assumption regarding cooperative hunting, two or more veloci-
raptors should have an insurmountable advantage, barring earlier detection.
Finally, we discuss an alternative approach, outlining a genetic program-
ming solution that would evolve optimal strategies for both animals. We begin
with the primitives required to evolve such a solution, and we discuss the na-
ture of the evolution required to produce optimal solutions. We show that the
evolutionary traits identified by this supposition mirror the known traits.
Background
Velociraptor, member of genus Theropod, lived in Central and East Asia dur-
ing the Late Cretaceous period ( to million years ago). It was a fairly
The UMAP Journal 18 (3) (1997) 243–254.
c Copyright 1997 by COMAP,Inc. All rights reserved.
Permission to make digital or hard copies of part or all of this work for personal or classroom use
is granted without fee provided that copies are not made or distributed for profit or comm