3.3: The following system of equations is a model for the populations of two species that compete for limited resources. x1) = 2x(1 - ) - xy y'(1) = 3y(1 – ) – 2.xy. Find and sketch the nullclines and find any equilibrium values. Use the nullclines to sketch the phase plane, indicating the trajectories of several possible solution. Based on your sketch, what can you say about the stability of the equilibria?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3.3: The following system of equations is a model for the populations of two species that compete
for limited resources.
x'(t) = 2x(1 –
- )- »
- xy
y'(1) = 3y (1 –
) –
- 2.xy.
Find and sketch the nullclines and find any equilibrium values. Use the nullclines to sketch the
phase plane, indicating the trajectories of several possible solution. Based on your sketch, what can
you say about the stability of the equilibria?
Transcribed Image Text:3.3: The following system of equations is a model for the populations of two species that compete for limited resources. x'(t) = 2x(1 – - )- » - xy y'(1) = 3y (1 – ) – - 2.xy. Find and sketch the nullclines and find any equilibrium values. Use the nullclines to sketch the phase plane, indicating the trajectories of several possible solution. Based on your sketch, what can you say about the stability of the equilibria?
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