Duff Campbell - USMA at West Point
A Bifurcation Problem in Differential Equations
The logistic model may often be used to model population growth. That model is dP/dt = k P (1-P/N) where P = population at time t, t = time, k = growth rate parameter, and N is the carrying capacity. This model may be modified to take into account harvesting: one such model is dP/dt = k P (1-P/N) - H. Using qualitative techniques, it is easy to see that this model undergoes a qualitative difference, or "bifurcation", at H = k N/4. The results of a student lab which studied the effect of periodic harvesting,
dP/dt = k P (1-P/N) - H (1 - sin(2 pi t)),
are explained and amplified on. This talk is accessible to anyone with an exposure to differential equations. In fact, if you know that dP/dt > 0 means "P is increasing" and dP/dt < 0 means "P is decreasing", you will understand what is going on.
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