# Non-dimensionalising Differential Equations

Two species with populations N1(t) and N2(t) interact according to the model:

(dN_1/d_t)=r_1N_1(1-(N_1/K_1) - b_12(N_2/K_1),

(dN_2/d_t)=r_2N_2(1-b_21(N_1/K_2),

Non-dimensionalise the system (7) so that:

(d_u/d_t) = u (1- u - au), (d_u/d_t) = pv (1-Bu),

finding explicit formulae for the new constraints p, a, and B in terms of the constants of equation (7).

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#### Solution Preview

See attached

The equations are:

(1.1)

We set the non dimensional variables

(1.2)

Where are scaling constants with the appropriate dimensions.

Then, using the ...

#### Solution Summary

The solution shows, in details, how to find appropriate scaling factors in order to convert species population model differential equations to non-dimensional equations.

$2.19