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Use the eigenvalue approach to analyze all equilibria of the given Lotka-Volterra models of interspecific competition. dN1 N1 1.1- N2 = 5N, |1- dt 19 19 dN2 N2 N1 = 6N21- 0.8- 22 dt 22 ...... Select the correct answer below. O A. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally stable. The equilibrium (0, 22) is unstable. The equilibrium at the non-trivial solution cannot be analyzed. O B. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution is locally stable. O C. The trivial equilibria (0, 0) is stable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed. O D. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed.

Use the eigenvalue approach to analyze all equilibria of the given Lotka-Volterra models of interspecific competition. dN1 N1 1.1- N2 = 5N, |1- dt 19 19 dN2 N2 N1 = 6N21- 0.8- 22 dt 22 ...... Select the correct answer below. O A. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally stable. The equilibrium (0, 22) is unstable. The equilibrium at the non-trivial solution cannot be analyzed. O B. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution is locally stable. O C. The trivial equilibria (0, 0) is stable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed. O D. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed.

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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Use the eigenvalue approach to analyze all equilibria of the given Lotka-Volterra models of interspecific competition. dN, = 5N1 N1 1 19 N2 1.1. 19 dt N2 0.8 N1 dN2 6N2 1- 22 dt 22 Select the correct answer below. O A. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally stable. The equilibrium (0, 22) is unstable. The equilibrium at the non-trivial solution cannot be analyzed. B. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution is locally stable. O C. The trivial equilibria (0, 0) is stable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed. D. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. 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. dN, = 5N1 N1 1 19 N2 1.1. 19 dt N2 0.8 N1 dN2 6N2 1- 22 dt 22 Select the correct answer below. O A. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally stable. The equilibrium (0, 22) is unstable. The equilibrium at the non-trivial solution cannot be analyzed. B. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution is locally stable. O C. The trivial equilibria (0, 0) is stable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed. D. The trivial equilibria (0, 0) is unstable. The equilibrium (19, 0) is locally unstable. The equilibrium (0, 22) is locally stable. The equilibrium at the non-trivial solution cannot be analyzed.
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