FobelloE

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

$y=\frac{aK}{\alpha}\sqrt{\frac{c}{a}}\mathrm{sin}(\sqrt{act})$ . Where y is the population of the prey and predator population with negligible initial condition.

The given equation of predator population is$x=\frac{cK}{\gamma}\mathrm{cos}(\sqrt{act}).$

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

From the sinusoidal function$y={y}_{m}\mathrm{sin}(\omega t)$ the time period can be calculated as $T=2\pi .$

By comparing the given equation with sinusoidal function, the time period is$T=\frac{2\pi}{\sqrt{ac}}$

Taking into consideration the values of the system,$c=0.75,a=1,\alpha =0.5,\gamma =0.25.$

Then calculation of time period is$T=\frac{2\pi}{\sqrt{ac}}$

$T=\frac{2\pi}{\sqrt{ac}}$

$=\frac{2\pi}{\sqrt{1\times 0.75}}$

$\approx 7.25$

Therefore, the period of the oscillations of the prey and predator population is$T=7.25.$

The given equation of predator population

The given equation of predator population is

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

From the sinusoidal function

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

Taking into consideration the values of the system,

Then calculation of time period is

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

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