solve question 8 8. Consider the population modeldydt== 3y - y² - 2.This is a harvesting equation with a harvesting rate of 2. Find the steady states and theirstability, and interpret your answer in terms of the population model. Is this overhar-vesting, underharvesting, or critical harvesting?9. Repeat the previous question with the equationdydt3y - y² - 4.Find the steady states (if any) and their stability. Is this overharvesting, underharvesting,or critical harvesting?

The given population model is .Here the harvesting rate is .To find the steady states and their…

Answered: 8. Consider the population model dy dt…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...

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23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
Population equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates from the equilibrium it tends to diverge from it even further, this is an unstable equilibrium. Think of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following. dN Use a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability. Enter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.) stable N = unstable N =
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8. Consider the population model dy dt = 3y - y² - 2. This is a harvesting equation with a harvesting rate of 2. Find the steady states and their stability, and interpret your answer in terms of the population model. Is this overhar- vesting, underharvesting, or critical harvesting?