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.

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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(a) Find all equilibria in model (1) and explain biological meaning of each of them. Which
of the equilibria are biologically feasible?
Transcribed Image Text:(a) Find all equilibria in model (1) and explain biological meaning of each of them. Which of the equilibria are biologically feasible?
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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