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/courses/course-vUB The parameter e, which might for example represent the number of boats allowed in the fishing fleet, is to be considered constant in time, but we'll be interested in various values for that constant. (1a) Describe the phase line for the system when there is no harvesting: effort e = 0, Use the following notation. If the phase line you would draw by hand looked like this: → -2 >0<1/5>1< 3 S,U,S you would enter">-2<3>", using > to mean increasing, and

/courses/course-vUB The parameter e, which might for example represent the number of boats allowed in the fishing fleet, is to be considered constant in time, but we'll be interested in various values for that constant. (1a) Describe the phase line for the system when there is no harvesting: effort e = 0, Use the following notation. If the phase line you would draw by hand looked like this: → -2 >0<1/5>1< 3 S,U,S you would enter">-2<3>", using > to mean increasing, and

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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/courses/course-v1:UBx+2022_i+sp||ll92024_Cheliyavarig,coul If the phase line you would draw by hand looked like this: The parameter e, which might for example represent the number of boats allowed in the fishing fleet, is to be considered constant in time, but we'll be interested in various values for that constant. (1a) Describe the phase line for the system when there is no harvesting: effort e = 0, Use the following notation. >0<1/5>1< dP dt PH = P (1 – P) (5P − 1) – eP Ba you would enter"> -2 < 3 >", using > to mean increasing, and < to mean decreasing. If the equation had no critical points and solutions were decreasing everywhere, you would enter just "<". s,u,s (1b) Describe the equilibria you have found in part (1a) as stable (s) or unstable (u). Enter a comma-separated list of 's's and 'u's in the order corresponding to your answer in (1a). (2) Describe the phase line for the system when the harvesting effort e = 2. (3) The phase lines in parts 1 and 2 are qualitatively different. They must "morph" into each other somehow. Find the e-value for the transitional case, and describe the corresponding phase line. W
Transcribed Image Text:/courses/course-v1:UBx+2022_i+sp||ll92024_Cheliyavarig,coul If the phase line you would draw by hand looked like this: The parameter e, which might for example represent the number of boats allowed in the fishing fleet, is to be considered constant in time, but we'll be interested in various values for that constant. (1a) Describe the phase line for the system when there is no harvesting: effort e = 0, Use the following notation. >0<1/5>1< dP dt PH = P (1 – P) (5P − 1) – eP Ba you would enter"> -2 < 3 >", using > to mean increasing, and < to mean decreasing. If the equation had no critical points and solutions were decreasing everywhere, you would enter just "<". s,u,s (1b) Describe the equilibria you have found in part (1a) as stable (s) or unstable (u). Enter a comma-separated list of 's's and 'u's in the order corresponding to your answer in (1a). (2) Describe the phase line for the system when the harvesting effort e = 2. (3) The phase lines in parts 1 and 2 are qualitatively different. They must "morph" into each other somehow. Find the e-value for the transitional case, and describe the corresponding phase line. W
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