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 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.
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