The Logistic Growth Differential Equation

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Ah Logistic Growth, my favourite! This autonomous first-order differential equation is great because it has two equilibrium solutions, one unstable and one stable, and then a nice curve that grows between these two. The idea is if what you are studying has two equilibria, logistic growth can often represent a nice way to smoothly transition from one to the other. It is particularly useful for things like modelling populations with a carrying capacity.

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