Non-dimensionalising Differential Equations
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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 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.
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 ...
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