dN1 N1 (2 – N1 – 2N2) = f(N1, N2), dt (1) dN2 = N2(3 – N2 – 3N1) = 9(N1, N2), dt where N1 = N1(t) and N2 = N2(t) are the population densities of the competing species.

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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(b) For each of the equilibria write a Jacobian matrix and find its eigenvalues. Classify
all equilibria points.
Transcribed Image Text:(b) For each of the equilibria write a Jacobian matrix and find its eigenvalues. Classify all equilibria points.
Interaction of two species of squirrels fiercely competing for the same ecological niche on
an island is described by Lotka-Volterra-Gause equations
dN1
N1(2 – N1 – 2N2) = f(N1, N2),
dt
(1)
dN2
N2(3 – N2 – 3N1) = g(N1, N2),
dt
where N1 = N1(t) and N2 = N2(t) are the population densities of the competing species.
Transcribed Image Text:Interaction of two species of squirrels fiercely competing for the same ecological niche on an island is described by Lotka-Volterra-Gause equations dN1 N1(2 – N1 – 2N2) = f(N1, N2), dt (1) dN2 N2(3 – N2 – 3N1) = g(N1, N2), dt where N1 = N1(t) and N2 = N2(t) are the population densities of the competing species.
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