The competition for pic-a-nic baskets at the Jellystone Park Yogi Bear, Boo-Boo,

Question

The competition for pic-a-nic baskets at the Jellystone Park Yogi Bear, Boo-Boo, and other ursine denizens of the Jellystone Park often compete with the park's visitors for their favorite food- the content of visiters' picnic baskets. In response to numerous complaints the park's management, worrying that Yogi and friends might be overly aggressive in their foraging activity and are thus driving visitors away from the park, asked Ranger Smith to look into this matter. Let v(t) denote the average daily number of visitors to the park, and led y(t) denote the park's bear population. According to Ranger Smith's study, this competing-species (i.e., the two populations compete over the same resource, but otherwise do not prey upon each other) relationship can be described by the nonlinear system: v' = 3200v - 10v2 - 5vy y' = 1800y - 15y2 - 4vy In the absence of tourists equation ( that is ,if the park were to be closed to visitors set v+0 and solve the resulting logistic equation for y), determine the maximum sustainable bear population. Find the systems critical points (there are 4) In a competing = species is possible if there exists a stable or asymptotically stable critical point in the first quadrant. Linearize the system's first quadrant critical point, and determine its type and stability. Based on your result are Yogi and his bear friends being overly aggressive, or are the visitors tolerating the misbehaviours of the bears of the Jellystone Park

Explanation / Answer

a)

now put v=0

hence

y'=1800y-15y^2

put y'=0 to maximize

hence

y=120

please rate the answer

then I would answer the rest of parts

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