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FobelloE

Answered question

2020-12-01

Calculate the period of prey and predator populations using the approximation if

T = 7.25

lamanocornudaW

Skilled2020-12-02Added 85 answers

Step 1
The given equation of predator population

y = \frac{a K}{α} \sqrt{\frac{c}{a}} \sin (\sqrt{a c t})

. Where y is the population of the prey and predator population with negligible initial condition.
The given equation of predator population is

x = \frac{c K}{γ} \cos (\sqrt{a c t}) .

Where x is the population of the prey with negligible initial condition.
From the sinusoidal function

y = y_{m} \sin (ω t)

the time period can be calculated as

T = 2 π .

By comparing the given equation with sinusoidal function, the time period is

T = \frac{2 π}{\sqrt{a c}}

Taking into consideration the values of the system,

c = 0.75, a = 1, α = 0.5, γ = 0.25 .

Then calculation of time period is

T = \frac{2 π}{\sqrt{a c}}

T = \frac{2 π}{\sqrt{a c}}

= \frac{2 π}{\sqrt{1 \times 0.75}}

\approx 7.25

Therefore, the period of the oscillations of the prey and predator population is

T = 7.25 .

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