# project

UU7777

trajectories.  Explain the meanings of the direction arrows, the trajectories, and the equilibriumpoint (in terms of rabbits and foxes).  How can one tell from the picture which population isthe predator and which is the prey?  In other words, how can we tell whether foxes eat rabbitsor rabbits eat foxes?Step 2.  Assume that at time 0, the preserve is stocked with 200 rabbits and 50 foxes.  Fora second picture, obtain a plot of both the rabbit and fox populations versus time (using thegraph* menu of the display screen).  Discuss the behavior of the populations over time.  Yourdiscussion should include estimates of the minimums and maximums of each population andwhen they occur.  What is the period of oscillation of the rabbit and fox populations?  Is itreasonable that such populations would be cyclical?  If, at a low point in the fox population, anillness would wipe out the remaining foxes, what would then happen to the rabbit populationaccording to the model?  Would it still be cyclical?Step 3.  Assume you are managing the preserve discussed in Step 2.  You recognize that therabbit and fox populations are quite unstable, with populations swinging dramatically betweenhigh and low values, so you plan to trap and remove a number of foxes.  Based on the pictures,at what point should you take this step and about how many foxes should you remove in orderto  achieve  the  goal  of  making  the  population  somewhat  more  stable?   Discuss  options  andobserve what happen if the timing or the number is wrong.  At what point on the trajectorywould the removal of foxes have the most destabilizing effect?2

Grading Rubric for ProjectsMathematical Writing assignments involve writing skills as well as mathematical skills, sothe evaluation criteria include both.  The criteria for this assignment are:1.  Comprehensiveness (30%):(a)  all aspects of the assignment are covered;(b)  all questions stated in the assignment are answered;(c)  explanations are thorough;(d)  supporting arguments are included.2.  Mathematical Correctness (30%):(a)  appropriate mathematical and computer methods are used;(b)  mathematical steps are correct;(c)  mathematical logic is clear.3.  Expository Quality (30%):(a)  organization is logical and includes an introduction and conclusion;(b)  transitions from one idea to the next are smooth;(c)  mathematical work and computer output are smoothly integrated into the text;(d)  mathematical statements are presented within complete sentences;(e)  any figures or computer output are described in the exposition;(f)  grammar, spelling and punctuation are correct.4.  Extras (10%):(a)  the overall impact is positive;(b)  creativity and innovation are apparent.

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### project（1）

All members of the group are to be involved in the computer part as well as in the write-up.You should respond to the questions posed below and write your report in the form of a paper with an …