mcm1997A The Velociraptor Problem 疾走龙属问题美国数学建模 - matlab数学建模

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标题：mcm1997A The Velociraptor Problem 疾走龙属问题美国数学建模
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(MCM 1997A)

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 or larger packs. Unfortunately, there is no way to observe its hunting behavior in the wild as can be done with modern mammalian predators. A group of paleontologists has approached your 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.

The average adult velociraptor was 3 meters long with a hip height of 0.5meters 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.

Suppose that Velociraptor prey on Thescelosaurus neglectus, a herbivorous biped approximately the same size as the Velociraptor. A biomechanical analysis of a fossilized thescelosaurus indicates that if could run at a speed of about 50km.hr. for long periods of time.

Part1

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 thecelosaurus can always detect the velociraptor when in 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.

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 and limitations given in Part 1.

疾走龙问题(美国竞赛1997年A题)

Velociraptor，Velociraptor mongo1iensis是生活在距今约7500万年前后白垩纪(译注：白垩纪为距今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。

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迫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。

平均的成年Velociraptor长3米，髋高0.5米，重约45公斤。据估计，这种动物跑得非常快，速度可达60公里/小时，持续约15秒。在以这种速度开始助冲刺后．它要停下来在其肌肉中积聚乳酸以恢复体力。

假设Velociraptor摘食一种称为Thescelosaurus(太西龙届)neglectus的大小与Velociraptor差不多的双足食草动物。从Thescelosaurus化石的生物力学分析得知Thescelosaurus可以50公里/小时的速度长时间奔跑。

第1部分

假设Velociraptor是一只独居的猎食其他动物的野兽，试设计一个单个的Velociraptor潜近猎物并追猎一只单个的Thescelosaurus的策略以及被追捕物逃避迟捕的策略的数学模型。假设当Vclociraptor潜近15米内时，Thescelosaurus总能觉察到，根据栖息地及气候的条件不同，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Vclociraptor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，Thescelosaurus却是极其灵活的．其拐弯半径只有0.5米。

第2部分

更现实地假设Vclociraptor是成对外出追猎，试设计一个新的关于成对的Vclociraptor潜近猎物并追猎一只单个的Thescelosaurus的策略以及被追捕物逃避追捕的策略的数学模型。利用第1部分给出假定和限制。

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mcm1997A The Velociraptor Problem 疾走龙属问题 .doc