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?
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.