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93. Logistic Equilibrium with Allee Effect A population whose growth is affected by the Allee effect is modeled using the dif- ferential equation: NP dt N rN(N – a) ( 1 - K = where r, a, k are all positive constants and a < K. The equilibria of this equation are N = 0, N = a, and N = K. Use the eigenvalue method to classify whether each of these equilibria is stable or unstable. %3D

93. Logistic Equilibrium with Allee Effect A population whose growth is affected by the Allee effect is modeled using the dif- ferential equation: NP dt N rN(N – a) ( 1 - K = where r, a, k are all positive constants and a < K. The equilibria of this equation are N = 0, N = a, and N = K. Use the eigenvalue method to classify whether each of these equilibria is stable or unstable. %3D

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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93. Logistic Equilibrium with Allee Effect A population whose growth is affected by the Allee effect is modeled using the dif- ferential equation: dN = rN(N = a) (1 – ) dt K where r, a, k are all positive constants and a < K. The equilibria of this equation are N = 0, N = a, and N = K. Use the eigenvalue method to classify whether each of these equilibria is stable or unstable.
Transcribed Image Text:93. Logistic Equilibrium with Allee Effect A population whose growth is affected by the Allee effect is modeled using the dif- ferential equation: dN = rN(N = a) (1 – ) dt K where r, a, k are all positive constants and a < K. The equilibria of this equation are N = 0, N = a, and N = K. Use the eigenvalue method to classify whether each of these equilibria is stable or unstable.
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