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Sketch the phase portrait of system (1) in the biologically sensible region, i.e. identify all relevant equilibria in the phase plane and sketch a few typical trajectories clearly indicating with arrows the direction of the phase trajectories.

Sketch the phase portrait of system (1) in the biologically sensible region, i.e. identify all relevant equilibria in the phase plane and sketch a few typical trajectories clearly indicating with arrows the direction of the phase trajectories.

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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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.
(c) Sketch the phase portrait of system (1) in the biologically sensible region, i.e. identify all relevant equilibria in the phase plane and sketch a few typical trajectories clearly indicating with arrows the direction of the phase trajectories.
Transcribed Image Text:(c) Sketch the phase portrait of system (1) in the biologically sensible region, i.e. identify all relevant equilibria in the phase plane and sketch a few typical trajectories clearly indicating with arrows the direction of the phase trajectories.
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