Consider the system (i) in Problem 1, and assume now tha
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Consider the system (i) in Problem 1, and assume now that both x and y are harvested, with efforts E1 and E2, respective
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Consider the system (i) in Problem 1, and assume now that both x and y are harvested, with efforts E1 and E2, respectively. Then the modified equations are dx dt = x(1 ? E1 ? x ? y), (v) dy dt = y(0.75 ? E2 ? y ? 0.5x). (a) When E1 = E2 = 0, there is an asymptotically stable node at (0.5, 0.5). Find conditions on E1 and E2 that permit the continued long-term survival of both species. (b) Use the conditions found in part (a) to sketch the region in the E1E2-plane that corresponds to the long-term survival of both species. Also identify regions where one species survives but not the other, and a region where both decline to extinction.
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