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Here is a fish-population model incorporating the effects of fish not finding mates if the population is too smalI, the death rate going up as the population increases, and of the population being harvested with "effort" e: dP —D Р(1— Р) (2Р — 1) — еР dt 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. (la) Sketch 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 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 "<". (Ib) Describe the equilibria you have found in part (la) 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 (la).

Here is a fish-population model incorporating the effects of fish not finding mates if the population is too smalI, the death rate going up as the population increases, and of the population being harvested with "effort" e: dP —D Р(1— Р) (2Р — 1) — еР dt 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. (la) Sketch 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 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 "<". (Ib) Describe the equilibria you have found in part (la) 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 (la).

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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Here is a fish-population model incorporating the effects of fish not finding mates if the population is too small, the death rate going up as the population increases, and of the population being harvested with "effort" e: dP — Р (1- Р) (2Р — 1) — еР dt 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. (la) Sketch 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 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 "<". (1b) Describe the equilibria you have found in part (la) 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 (la).
Transcribed Image Text:Here is a fish-population model incorporating the effects of fish not finding mates if the population is too small, the death rate going up as the population increases, and of the population being harvested with "effort" e: dP — Р (1- Р) (2Р — 1) — еР dt 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. (la) Sketch 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 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 "<". (1b) Describe the equilibria you have found in part (la) 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 (la).
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