The DE is Insect Outbreak Model: Spruce Budworn with Ludwig's predation model(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dN}{dt}=r_BN\left(1-\frac{N}{K_B}\right)-\frac{BN^2}{A^2+N^2}[/tex]

[itex]r_B[/itex] is the linear birth rate

[itex]K_B[/itex] is the carrying capacity

The last term is predation

[itex]A[/itex] is the threshold where predation is switched on

[itex]A,K_B,N,r_B[/itex] has the dimension [itex](\text{time})^{-1}[/itex]

[itex]B[/itex] has the dimension [itex]N(\text{time})^{-1}[/itex]

Nondimensional quantities

[tex]u=\frac{N}{A}, \ r=\frac{Ar_B}{B}, \ q=\frac{K_B}{A}, \ \tau=\frac{Bt}{A}[/tex]

How were this substitutions decided on?

I see that u,q is nondimensional since they cancel, but r and tau I don't get it.

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# Nondimensional quantities

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