8.2-1ab) Denote by p= p(t) the fraction of occupied sites in the patchy habitat model, and assume that= 0.5p(1- p) - 1.2p for t2 0. Complete parts (a) through (c).(a) Set g(p) = 0.5p(1- p) – 1.2p. Graph g(p) for pE[0, 1].O A.В.'C.O D.Ag(p)1-A9(p)1-A9(p)A9(p)-2-(b) Find all equilibria of g(p) = 0.5p(1 - p) - 1.2p that are in [0, 1]. Use your graph in (a) to determine their stability. (b) Find all equilibria of g(p) = 0.5p(1- p) - 1.2p that are in [0, 1]. Use your graph in (a) to determine their stability.O A. The stable equilibria are p=and the unstable equilibria are p=(Type an integer or a decimal. Use a comma to separate answers as needed.)B. The unstable equilibria are p =|There are no stable equilibria.(Type an integer or a decimal. Use a comma to separate answers as needed.)O C. The stable equilibria are p= There are no unstable equilibria.(Type an integer or a decimal. Use a comma to separate answers as needed.)O D. There are no equilibria.

Name: 8.2-1ab) Denote by p= p(t) the fraction of occupied sites in the patch
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: 8.2-1ab) Denote by p= p(t) the fraction of occupied sites in the patchy habitat model, and assume that= 0.5p(1- p) - 1.2p for t2 0. Complete parts (a) through (c).(a) Set g(p) = 0.5p(1- p) – 1.2p. Graph g(p) for pE[0, 1].O A.В.'C.O D.Ag(p)1-A9(p)1-A9

Now consider the phase-plate of the solution curve : From this sketch it appears that solutions that start “near” p=0 all move towards it as p increases and so p=0 is an stable equilibrium solution and solutions that start “near” p=-1.4 all move away from it as p increases and so p=-1.4 is an unstable equilibrium solution.As the question is asked to determine the equilibria in the interval [0,1], we have the solution as option C C) The stable equilibria is p=0 , there is no unstable equilibria.