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(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 (i) (w, r) = (12 12 the population of worms, w is increasing and the population of robins, r is decreasing (ii) (w, r) = ( 32 the population of worms, w is and the population of robins, r is increasing (iii) (w, r) = = 0.5 12 increasing 1 0.5 ) is in a second region, where ) is in a third region, where

(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 (i) (w, r) = (12 12 the population of worms, w is increasing and the population of robins, r is decreasing (ii) (w, r) = ( 32 the population of worms, w is and the population of robins, r is increasing (iii) (w, r) = = 0.5 12 increasing 1 0.5 ) is in a second region, where ) is in a third region, where

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 r and worms w, dr dt r = 1 (a) What are the (non-zero) nullclines for this system? W= 1 dw dt (i) (w, r) = ( 12 the population of worms, w is and the population of robins, r is decreasing 12 increasing (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 " (ii) (w, r) = ( 32 the population of worms, w is and the population of robins, r is increasing 12 increasing (iv) (w, r) = ( the population of worms, w is and the population of robins, r is = w ― wr, - " (iii) (w, r) = ( 0.5 the population of worms, w is and the population of robins, r is decreasing 0.5 increasing and -r + rw. ) is in a second region, where ) is in a third region, where ) is in the fourth region, where
Transcribed Image Text:Consider the equations describing the interactions of robins r and worms w, dr dt r = 1 (a) What are the (non-zero) nullclines for this system? W= 1 dw dt (i) (w, r) = ( 12 the population of worms, w is and the population of robins, r is decreasing 12 increasing (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 " (ii) (w, r) = ( 32 the population of worms, w is and the population of robins, r is increasing 12 increasing (iv) (w, r) = ( the population of worms, w is and the population of robins, r is = w ― wr, - " (iii) (w, r) = ( 0.5 the population of worms, w is and the population of robins, r is decreasing 0.5 increasing and -r + rw. ) is in a second region, where ) is in a third region, where ) is in the fourth region, where
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