2. Consider the prey-predator model with a = 3, b = 1, c = 6, q = r = s = 1 The predator-prey model is described by the following system of equations. Function x(t) is the population of prey at time t. Function y(t) is the population of predators at time t. dx dt dy dt = x(a - by — cx) = = y(−q+rx − sy) The equilibrium points are (0,0), (0,-2), (2,0), (α, ß) where α = as+bq cs+br' β -cq+ar = cs+br (a). Determine and classify all equilibria (node, saddle, spiral, center, stable or unstable) (b). Sketch the phase portrait using the linear systems (do not calculate eigenvectors). What happens to populations when the time increases? Note: Since x(t) and y(t) represent populations, x > 0 and y ≥ 0.
2. Consider the prey-predator model with a = 3, b = 1, c = 6, q = r = s = 1 The predator-prey model is described by the following system of equations. Function x(t) is the population of prey at time t. Function y(t) is the population of predators at time t. dx dt dy dt = x(a - by — cx) = = y(−q+rx − sy) The equilibrium points are (0,0), (0,-2), (2,0), (α, ß) where α = as+bq cs+br' β -cq+ar = cs+br (a). Determine and classify all equilibria (node, saddle, spiral, center, stable or unstable) (b). Sketch the phase portrait using the linear systems (do not calculate eigenvectors). What happens to populations when the time increases? Note: Since x(t) and y(t) represent populations, x > 0 and y ≥ 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Transcribed Image Text:2. Consider the prey-predator model with
a = 3, b = 1, c = 6, q = r = s = 1
The predator-prey model is described by the following
system of equations. Function x(t) is the population of
prey at time t. Function y(t) is the population of
predators at time t.
dx
dt
dy
dt
= x(a - by — cx)
=
= y(−q+rx − sy)
The equilibrium points are
(0,0), (0,-2), (2,0), (α, ß)
where
α =
as+bq
cs+br'
β
-cq+ar
=
cs+br
(a). Determine and classify all equilibria (node, saddle,
spiral, center, stable or unstable)
(b). Sketch the phase portrait using the linear systems (do
not calculate eigenvectors). What happens to
populations when the time increases?
Note: Since x(t) and y(t) represent populations, x > 0
and y ≥ 0.
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