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I am taking course on dynamical systems and I am asked to show that the growth rate of a population $N'/N=r-a(N-b)^2$ demonstrates the Allee effect if $r$, $a$, and $b$ satisfy certain constraints, which I must determine.

I came to the conclusion that $a,b,r>0$ for the effect to be demonstrated.

I would like to know if this is correct. Also, assuming it is, I used brute force testing in order to come to this conclusion and I am wondering if there is a better way of showing it.

Thanks!

Rob
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    Checking the definition should allow you to show analytically (not by brute force testing, whatever that means) that the condition for a strong Allee effect is not $a,b,r>0$. Or are you interested in a weak Allee effect? Please explain and show much more clearly what you did. – Did Sep 19 '16 at 11:29
  • i took a,b,r is less, greater, and equal to zero, plotted every permutation (brute force). There must be a better way of solving. Also, we haven't discussed the difference between weak and strong allee effecr. The definition given to me in the problem is "where growth is greatest at intermediate values of N." – Rob Sep 19 '16 at 13:25
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    I feel that reading carefully the WP page might help you: https://en.wikipedia.org/wiki/Allee_effect – Did Sep 19 '16 at 13:54

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