Population growth model
The simple population growth model, (because of limitation on resources, pollution, ...) is unsatisfactory over a 'long' period. We might look at
(which of course ignores seasonal and other variations with time). Mathematically one of the simplest assumptions we can make is that k(y) decreases linearly as y increases. In this case (1) may be written in the form
where k and K are constants.
a) i) Equation (2) has two constant (stationary) solutions. What are they?
I'm not sure how to calculate this. Do I have to solve the ODE? Or is there an obvious method? Thanks.
Hmm, I think I get it now. I just need find values of 'y' to make the RHS zero?
This is worth solving, separate, decompose with partial fractions and integrate.
Originally Posted by Glitch
Then look at solutions for
Ok, I tried to do that, and I got this:
So we get:
A = 1
= kt + C
Take the exponential of each side:
Is this right so far? Thanks.
However, to answer the question asked, "i) Equation (2) has two constant (stationary) solutions. What are they?", a "stationary solution" is a constant solution, dy/dt= 0 so, yes, just set the right side of the equation equal to 0: solve .