Purchase Solution

Non-dimensionalising Differential Equations

Not what you're looking for?

Ask Custom Question

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).

Attachments
Purchase this Solution

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 ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.