A remote national park is inhabited by wolves and deers. The following informati

Question

A remote national park is inhabited by wolves and deers. The following information is provided by the park rangers:  Every pair of deers normally produces 3 calves per year.  Wolves hunt deers for food: every wolf eats 0.5% of the current population of deers every year.  Every year, 14% of all wolves die or leave the park.  Wolves' breeding rate is proportional to the current population of deers. For example, in the last year there were 600 deers in the park, and the population of wolves increased by 12%. (1) Suggest a reasonable model, i.e., a system of dierential equations describing the dynamic of these populations (see Lotka|Volterra equations) (2) Help the rangers to estimate the maximal expected numbers of deers and wolves in the park during the subsequent years (in the absence of other factors) provided that in the last year populations were 600 deers and 200 wolves. (3) The National Park Service (NPS) would like to maintain the most stable populations as possible. Advise NPS how many deers and wolves should they leave in the park for that purpose. (Assume that "no deers, no wolves" is not an option.)

Explanation / Answer

1)deer population :x & wolves is :y

x/2*3 -0.5y =current deer population

y - 0.14y + kx =current wolves population

k = 0.12xy/600

2) deerpopulation= 800

wolvespopulation= 196

3)optimise euations from part 1 to get answer

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