Consider the following variation of the Lotka-Volterra predator prey model N = N(a - BN - YP) P = P(-8 + €N) Assume a > SB. (a) Draw the nullclines assuming that a = 2 and 3 = 8 = e = y = 1 and determine the directions the vector field. (b) Show that the equilibria are (c) Show that is stable. δα (0,0), (,0), (2, -50) δα BS YE
Consider the following variation of the Lotka-Volterra predator prey model N = N(a - BN - YP) P = P(-8 + €N) Assume a > SB. (a) Draw the nullclines assuming that a = 2 and 3 = 8 = e = y = 1 and determine the directions the vector field. (b) Show that the equilibria are (c) Show that is stable. δα (0,0), (,0), (2, -50) δα BS YE
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![Consider the following variation of the Lotka-Volterra predator prey model
N= N(a - BN — 7P)
P = P(−8+ €N)
Assume a > Sß.
Y
(a) Draw the nullclines assuming that a = 2 and 3 = 8 = € = 7 = 1 and determine the directions of
the vector field.
(b) Show that the equilibria are
(c) Show that
is stable.
δα
(0,0), (2,0),
(23,0), (2 - 2/0)
Y
γε
δα
(3,9-00)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a130e85-11e7-4176-8379-853b51fd42e7%2F5563b1c5-7c7c-40a2-bca6-ba7288026c8b%2F5zghnem_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following variation of the Lotka-Volterra predator prey model
N= N(a - BN — 7P)
P = P(−8+ €N)
Assume a > Sß.
Y
(a) Draw the nullclines assuming that a = 2 and 3 = 8 = € = 7 = 1 and determine the directions of
the vector field.
(b) Show that the equilibria are
(c) Show that
is stable.
δα
(0,0), (2,0),
(23,0), (2 - 2/0)
Y
γε
δα
(3,9-00)
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