★★★[求助]1997美国数学建模A题“恐龙捕食”建模方法★★★

lanfengdi

<>求助1997美国数学建模A题“恐龙捕食”建模方法。这是我们的作业题，我考虑了一个多星期也没想出点头绪，恳请各位高人指点指点解题思路，小弟万分感激。</P>
<>英文原题</P>
<><B>1997 A - The Velociraptor Problem </B></P>
<P>　　The velociraptor, Velociraptor mongoliensis, was a predatory dinosaur that lived during the late Cretaceous period, approximately 75 million years ago. Paleontologists think that it was a very tenacious hunter, and may have hunted in pairs of larger packs. Unfortunately, there is no way to oversee its hunting behavior in the wild as can be done with modern mammalian predators. A group of paleontologists has approached our team and asked for help in modeling the hunting behavior of the velociraptor. They hope to compare your results with field data reported by biologists studying the behaviors of lions, tigers, and similar predatory animals. </P>
<P>  </P>
<P>　　The average adult velociraptor was 3 meters long with a hip height of 0.5 meters and an approximate mass of 45 kg. It is estimated that the animal could run extremely fast, at speeds of 60 km/hr., for about 15 seconds. After the initial burst of speed, the animal needed to stop and recover from a buildup of lactic acid in its muscles. </P>
<P>  </P>
<P>　　Suppose the velociraptor preyed on Thescelosaurus neglectus, a herbivorous biped approximately the same size as the velociraptor. A biomechanical analysis of a fossilized thescelosaurus indicates that it could run at a speed of about 50 km/hr. for long periods of time. </P>
<P>  </P>
<P>　　Part 1. Assuming the velociraptor is a solitary hunter, design a mathematical model that describes a hunting strategy for a single velociraptor stalking and chasing a single thescelosaurus as well as the evasive strategy of the prey. Assume that the thescelosaurus can always detect the velociraptor when it comes within 15 meters, but may detect the predator at even greater ranges (up to 50 meters) depending upon the habitat and weather conditions. Additionally, due to its physical structure and strength, the velociraptor has a limited turning radius when running at full speed. This radius is estimated to be three times the animal's hip height. On the other hand, the thescelosaurus is extremely agile and has a turning radius of 0.5 meters. </P>
<P>  </P>
<P>　　Part 2. Assuming more realistically that the velociraptor hunted in pairs, design a new model that describes a hunting strategy for two velociraptors stalking and chasing a single thescelosaurus as well as the evasive strategy of the prey. Use the other assumptions given in Part 1. </P>
<br>
<P>中文译题：</P>
<P>Veloclrptor，Velociraptor mongoliensis，是生活在距今约7500万年前晚白至纪（译注：白要纪为距今1.36~0.65亿年的地质年代，是中生代最后的纪）的一种食肉（捕食其他动物的）恐龙。<br>古生物学家认为这是一种非常顽强的猎食其他动物的野兽，而且可能是成对或成群地外出追猎。然而，不幸的是无法像观察现代哺乳食肉动物在野外是如何追猎其食物的行为那样，观察到Velociraptor在野外的追猎行为。一组古生物学家来到你们队请求你们在Velociraptor的追猎行为的建模方面给予帮助，他们希望把你们的结果与研究狮子、老虎及其他类似的食肉动物行为的生物学家的研究报告相比较。<br>成年的Velocirapotor平均长3米，髓高0.5米，体重约为45千克，据估计，这种动物跑得非常快，速度可达60千米/小时，持续时间约15秒，在一开始的突然加速后，它要停下来并在其肌肉中积聚乳酸以恢复体力。<br>假设Velocirapotor捕食一种称为（太西龙属）的大小与差不多的双足食草动物，从化石的生物力学分析得知可以50千米/小时的速度长时间奔跑。<br>第一部分<br>假设是一只独居的猎其他动物的野兽，试设计单个的潜近猎物并追猎一只单个策略以及被追捕物逃避追捕的策略的数学模型，假设当潜近到的15米范围内时，总能觉察到，根据栖息地及气候条件的不同，甚至在（多达50米的）更大的范围内觉察欲捕食它的动物的存在，此外，由于的身体结构及体能，它在全速奔跑时的拐弯半径是受到限制的，据估计，拐弯半径大约是其髋高的三倍，另一方面，却是极其灵活的。其拐弯半径只有0。5米。<br>第二部分<br>更现实地假设是成对外出追猎，试设计一个新的关于成对的Velociraptor潜近猎物并追猎一只单个的太西龙属的策略以及被追捕物逃避追捕的策略的数学模型，利用第一部分给出的假设和限制。</P>

[此贴子已经被作者于2005-12-19 22:23:43编辑过]