3. Two species with population sizes x and y evolve according to the following pair of...

 

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3. Two species with population sizes x and y evolve according to the following pair of coupled differential equations: dx dt dy dt 4x (5 - y), -y(1-x). (a) [5 Mark] Briefly explain what kind of system these equations describe and provide an inter- pretation for each of the various terms in these equations. (b) [5 Marks] Determine all of the equilibrium points for x, y. (c) [6 Marks] Find an approximate solution to these equations near to non-zero equilibrium. (d) [4 Marks] Comment on the behaviour of x, y in the four regions I: x > 1, y < 5, II: x > 1,y> 5 III: x < 1,y> 5, IV: x < 1, y < 5. 3. Two species with population sizes x and y evolve according to the following pair of coupled differential equations: dx dt dy dt 4x (5 - y), -y(1-x). (a) [5 Mark] Briefly explain what kind of system these equations describe and provide an inter- pretation for each of the various terms in these equations. (b) [5 Marks] Determine all of the equilibrium points for x, y. (c) [6 Marks] Find an approximate solution to these equations near to non-zero equilibrium. (d) [4 Marks] Comment on the behaviour of x, y in the four regions I: x > 1, y < 5, II: x > 1,y> 5 III: x < 1,y> 5, IV: x < 1, y < 5.

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a System Description and Term Interpretation These equations describe a predatorprey systemwhere x r... View the full answer