Consider the equations describing the interactions of robins r and worms w, dw dt (a) What are the (non-zero) nullclines for this system? W = r = (i) (w, r) = ( the population of worms, w is and the population of robins, r is (ii) (w, r) = ( the population of worms, w is and the population of robins, r is (iii) (w, r) = ( the population of worms, w is and the population of robins, r is =w-wr, (b) Your nullclines divide the phase plane into four regions. Give a sample point in each region, and indicate for that point wh populations is increasing or decreasing (by entering the word increasing or decreasing appropriate blank): ) is in one region, where (iv) (w, r) = ( the population of worms, w is and the population of robins, r is and ) is in a second region, where ) is in a third region, where dr dt ) is in the fourth region, where = -r+rw.
Consider the equations describing the interactions of robins r and worms w, dw dt (a) What are the (non-zero) nullclines for this system? W = r = (i) (w, r) = ( the population of worms, w is and the population of robins, r is (ii) (w, r) = ( the population of worms, w is and the population of robins, r is (iii) (w, r) = ( the population of worms, w is and the population of robins, r is =w-wr, (b) Your nullclines divide the phase plane into four regions. Give a sample point in each region, and indicate for that point wh populations is increasing or decreasing (by entering the word increasing or decreasing appropriate blank): ) is in one region, where (iv) (w, r) = ( the population of worms, w is and the population of robins, r is and ) is in a second region, where ) is in a third region, where dr dt ) is in the fourth region, where = -r+rw.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the equations describing the interactions of robins r and worms w,
dw
dt
(a) What are the (non-zero) nullclines for this system?
W =
r =
(i) (w, r) = (
the population of worms, w is
and the population of robins, r is
(ii) (w, r) = (
the population of worms, w is
and the population of robins, r is
(iii) (w, r) = (
the population of worms, w is
and the population of robins, r is
(b) Your nullclines divide the phase plane into four regions. Give a sample point in each region, and indicate for that point whether each of the
populations is increasing or decreasing (by entering the word increasing or decreasing appropriate blank):
) is in one region, where
"
=w-wr,
(iv) (w, r) = (
the population of worms, w is
and the population of robins, r is
and
is in a second region, where
) is in a third region, where
dr
dt
) is in the fourth region, where
==r+rw.
Notice what your conclusions about these four regions say about how the populations change with time.
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