Explore BrainMass
Share

Explore BrainMass

    Non-dimensionalising Differential Equations

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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).

    © BrainMass Inc. brainmass.com October 10, 2019, 7:27 am ad1c9bdddf
    https://brainmass.com/math/algebra/non-dimensionalising-differential-equations-582385

    Attachments

    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