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dN₁ dt dN₂ dt 5N₁ 1 N₁ 20 N₂ 17 9N₂ 1-- N₂ 20 N₁ 17 1.6- 0.6-

dN₁ dt dN₂ dt 5N₁ 1 N₁ 20 N₂ 17 9N₂ 1-- N₂ 20 N₁ 17 1.6- 0.6-

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Use the eigenvalue approach to analyze all equilibria of the given Lotka-Volterra models of interspecific competition. dN₁ N₁ N₂ dt 20 20 dN₂ N₂ N₁ dt 17 17 -= 5N₁ 1- = 9N₂ 1- -1.6 -0.6- Select the correct answer below. C O A. The trivial equilibria (0, 0) is unstable. The equilibrium (20, 0) is locally unstable. The equilibrium (0, 17) is locally stable. The equilibrium at the non-trivial solution is locally stable. OB. The trivial equilibria (0, 0) is stable. The equilibrium (20, 0) is locally unstable. The equilibrium (0, 17) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed. OC. The trivial equilibria (0, 0) is unstable. The equilibrium (20, 0) is locally unstable. The equilibrium (0, 17) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed. O D. The trivial equilibria (0, 0) is unstable. The equilibrium (20, 0) is locally stable. The equilibrium (0, 17) is unstable. The equilibrium at the non-trivial solution cannot be analyzed.
Transcribed Image Text:Use the eigenvalue approach to analyze all equilibria of the given Lotka-Volterra models of interspecific competition. dN₁ N₁ N₂ dt 20 20 dN₂ N₂ N₁ dt 17 17 -= 5N₁ 1- = 9N₂ 1- -1.6 -0.6- Select the correct answer below. C O A. The trivial equilibria (0, 0) is unstable. The equilibrium (20, 0) is locally unstable. The equilibrium (0, 17) is locally stable. The equilibrium at the non-trivial solution is locally stable. OB. The trivial equilibria (0, 0) is stable. The equilibrium (20, 0) is locally unstable. The equilibrium (0, 17) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed. OC. The trivial equilibria (0, 0) is unstable. The equilibrium (20, 0) is locally unstable. The equilibrium (0, 17) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed. O D. The trivial equilibria (0, 0) is unstable. The equilibrium (20, 0) is locally stable. The equilibrium (0, 17) is unstable. The equilibrium at the non-trivial solution cannot be analyzed.
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