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Differential Equationshard
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A population model is defined by dPdt=0.05P(1−P500)\frac{dP}{dt} = 0.05P(1 - \frac{P}{500})dtdP​=0.05P(1−500P​). If a constant harvesting rate HHH is introduced such that dPdt=0.05P(1−P500)−H\frac{dP}{dt} = 0.05P(1 - \frac{P}{500}) - HdtdP​=0.05P(1−500P​)−H, what is the bifurcation value of HHH at which the equilibrium points disappear?