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Interaction of two species of squirrels fiercely competing for the same ecologic an island is described by Lotka-Volterra-Gause equations

Interaction of two species of squirrels fiercely competing for the same ecologic an island is described by Lotka-Volterra-Gause equations

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 64EQ
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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 – 3N) = g(N1, N2), dt where N = N1(t) and N2 = N2(t) are the population densities of the competing species. (a) Find all equilibria in model (1) and explain biological meaning of each of them. Which of the equilibria are biologically feasible? (b) For each of the equilibria write a Jacobian matrix and find its eigenvalues. Classify all equilibria points.
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 – 3N) = g(N1, N2), dt where N = N1(t) and N2 = N2(t) are the population densities of the competing species. (a) Find all equilibria in model (1) and explain biological meaning of each of them. Which of the equilibria are biologically feasible? (b) For each of the equilibria write a Jacobian matrix and find its eigenvalues. Classify all equilibria points.
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