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dw dr w - wr, and -r+ rw. dt 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): (i) (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 ||

dw dr w - wr, and -r+ rw. dt 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): (i) (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 ||

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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interactions of worms (w) and robins (r)

dw dr w – wr, and = -r + rw. dt 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): () (w, г) — ( ) 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 Notice what your conclusions about these four regions say about how the populations change with time. ||
Transcribed Image Text:dw dr w – wr, and = -r + rw. dt 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): () (w, г) — ( ) 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 Notice what your conclusions about these four regions say about how the populations change with time. ||
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