Douglas C.

asked • 9d

Differentiate Logistic Growth equation dP/dt = A(P-m)*(M-P), where M is the carrying capacity, and m is the minimal amount

How can I rewrite this logistic growth equation into a differential equation of the form dP/dt = k(L-P), where L is the carrying capacity and k is a constant. I appreciate your help!

Dayv O.

tutor
dP/dt = kP(1-P/k) is most basic logistic growth and the question is about differentiation. Usually in Autonomous differential equation, Set DP/dt=0 for equilibrium P values. And use d(dP/dt)/dP to find stablilty. Are you sure you need dP/dt in K(L-P) terms because actually dP/dt=f(P^2)??
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9d

Dayv O.

tutor
I'd guess that d(dP/dt)/dP is desired which is -A(-(M+m)+2P)
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9d

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