Question

The following differential equations model a predictor/prey relationship between two species X and Y (the population sizes being given by x and y respectively): x? = -x/30000 + xy/(3 × 10?) y? = y/30000 - 2/(9 × 10?) y² - xy/(9 × 10?) (i) Which species, X or Y, represents the predator? Explain so. (ii) In the absence of species X (i.e. x = 0), find the populations for y at time t if y(0) = y? where y? > 0. Sketch the graph of y(t) against t for different values of y?. (iii) Find and classify the equilibrium points for the system.

          The following differential equations model a predictor/prey relationship between two species X and Y (the population sizes being given by x and y respectively):
x? = -x/30000 + xy/(3 × 10?)
y? = y/30000 - 2/(9 × 10?) y² - xy/(9 × 10?)

(i) Which species, X or Y, represents the predator? Explain so.
(ii) In the absence of species X (i.e. x = 0), find the populations for y at time t if y(0) = y? where y? > 0. Sketch the graph of y(t) against t for different values of y?.
(iii) Find and classify the equilibrium points for the system.

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The following differential equations model a predictor/prey relationship between two species X and Y (the population sizes being given by x and y respectively):
x? = -x/30000 + xy/(3 × 10?)
y? = y/30000 - 2/(9 × 10?) y² - xy/(9 × 10?)

(i) Which species, X or Y, represents the predator? Explain so.
(ii) In the absence of species X (i.e. x = 0), find the populations for y at time t if y(0) = y? where y? > 0. Sketch the graph of y(t) against t for different values of y?.
(iii) Find and classify the equilibrium points for the system.

Added by Tom-S H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/03/2023

Step 1

It seems there might be some formatting issues, but I will assume the equations are: $$\frac{dx}{dt} = 30000x - \frac{3}{108}xy$$ $$\frac{dy}{dt} = -30000y + \frac{9}{108}xy$$ Now, let's analyze the equations to determine which species is the predator. In the Show more…

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The following differential equations model a predictor/prey relationship between two species X and Y (the population sizes being given by x and y respectively): ẋ = -x/30000 + xy/(3 × 10⁸) ẏ = y/30000 - 2/(9 × 10⁸) y² - xy/(9 × 10⁷) (i) Which species, X or Y, represents the predator? Explain so. (ii) In the absence of species X (i.e. x = 0), find the populations for y at time t if y(0) = y₀ where y₀ > 0. Sketch the graph of y(t) against t for different values of y₀. (iii) Find and classify the equilibrium points for the system.

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