Calculate the period of prey and predator populations using the approximation if T = 7.25

FobelloE 2020-12-01 Answered
Calculate the period of prey and predator populations using the approximation if T=7.25
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lamanocornudaW
Answered 2020-12-02 Author has 85 answers
Step 1
The given equation of predator population
y=aKαcasin(act). Where y is the population of the prey and predator population with negligible initial condition.
The given equation of predator population is x=cKγcos(act).
Where x is the population of the prey with negligible initial condition.
From the sinusoidal function y=ymsin(ωt) the time period can be calculated as T=2π.
By comparing the given equation with sinusoidal function, the time period is T=2πac
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=2πac
T=2πac
=2π1×0.75
7.25
Therefore, the period of the oscillations of the prey and predator population is T=7.25.
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