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Phase Lines

Suppose you wish to model a population with a differential equation of the form dP/dt = f(p), where P(t) is the population at time t. Experiments have been performed on the population that give the following information:

? The population P = 0 remains constant.
? A population close to 0 will decrease.
? A population of P = 20 will increase.
? A population of P>100 will decrease.

I have drawn one phase line with the points 0, 20, & 100. The point 20 is a source and 100 is a sink. I have also been able to draw a rough sketch of this function. What I want to know is what other phase lines are possible here?


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Phase lines are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.