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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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)
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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