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dw = w - wr, dt dr and = -r + rw. dt (a) What are the (non-zero) nullclines for this system? w = r = (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): (1) (w, r) = ( ) is in one region, where the population of worms, w is and the population of robins, r is (ii) (w, r) = ( ) is in a second region, where the population of worms, w is and the population of robins, r is (iii) (w, r) = ( ) is in a third region, where the population of worms, w is and the population of robins, r is (iv) (w, r) = ( ) is in the fourth region, where the population of worms, w is and the population of robins, r is

dw = w - wr, dt dr and = -r + rw. dt (a) What are the (non-zero) nullclines for this system? w = r = (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): (1) (w, r) = ( ) is in one region, where the population of worms, w is and the population of robins, r is (ii) (w, r) = ( ) is in a second region, where the population of worms, w is and the population of robins, r is (iii) (w, r) = ( ) is in a third region, where the population of worms, w is and the population of robins, r is (iv) (w, r) = ( ) is in the fourth region, where the population of worms, w is and the population of robins, r is

Advanced Engineering Mathematics
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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Consider the equations describing the interactions of robins ? and worms ?

dw = w – Wur, dt dr and = -r + rw. dt (a) What are the (non-zero) nullclines for this system? w = r = (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): (1) (w, r) = ( ) is in one region, where the population of worms, u is and the population of robins, r is (i) (w, r) = ( ) is in a second region, where the population of worms, w is and the population of robins, r is (iii) (w, r) = ( ) is in a third region, where the population of worms, w is and the population of robins, r is (iv) (w, r) = ( ) is in the fourth region, where the population of worms, w is and the population of robins, r is Notice what your conclusions about these four regions say about how the populations change with time.
Transcribed Image Text:dw = w – Wur, dt dr and = -r + rw. dt (a) What are the (non-zero) nullclines for this system? w = r = (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): (1) (w, r) = ( ) is in one region, where the population of worms, u is and the population of robins, r is (i) (w, r) = ( ) is in a second region, where the population of worms, w is and the population of robins, r is (iii) (w, r) = ( ) is in a third region, where the population of worms, w is and the population of robins, r is (iv) (w, r) = ( ) is in the fourth region, where the population of worms, w is and the population of robins, r is Notice what your conclusions about these four regions say about how the populations change with time.
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