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## Homework Statement

The population of a country is divided in two groups:

People who live in rural areas (R(t)) and people who live in urban areas (U(t)).

People move from rural to urban areas with a rate m and from

urban to rural areas with rate n.

**a)**Introduce the fraction of people (Z(t)) who live in rural

areas as a new variable and derive an equation for it.

**b)**Find the steady state(s) of the equation for Z and the

stability condition.

## Homework Equations

R' = −mR + nU

U' = mR − nU.

## The Attempt at a Solution

a) So I don't really get this, but is the fraction Z(t) different from R(t)??

Anyways, I think it goes:

Z(t) = R(t) - U(t) / R(t)

how would i go about deriving it?

I am extremely confused. If anyone can just somehow reword it or something so that I can understand it that would be great.

b) If I could get Z(t) into differential form I can easily find the steady state, by just setting it = to 0.. so my problem really lies in the first part.