HW #4 problem 3: In this problem, you will investigate changes in the behavior of x, as predicted by the "logistic" model x,n+1 = r(1 – x„)xn caused by changes in the parameter value r or in the “initial" value x. Starting with x, = 0.25, look at the behavior of x1, x2, ., X50 for r = 2, then for r = 2.25, then for r = 2.5, and so on until r = 4. Where do you see important changes occur? Repeat this for x, = 0.3 and report where you see the greatest sensitivity to changes in the initial value. Using Excel or some similarly simple calculation system will make this problem more manageable. It may also be helpful to consider how the behaviors you observe compare to the “equilibrium states" xe for this model. You can determine these by solving x. = r(1 –xe)Xe

HW #4 problem 3: In this problem, you will investigate changes in the behavior of x, as predicted by the "logistic" model x,n+1 = r(1 – x„)xn caused by changes in the parameter value r or in the “initial" value x. Starting with x, = 0.25, look at the behavior of x1, x2, ., X50 for r = 2, then for r = 2.25, then for r = 2.5, and so on until r = 4. Where do you see important changes occur? Repeat this for x, = 0.3 and report where you see the greatest sensitivity to changes in the initial value. Using Excel or some similarly simple calculation system will make this problem more manageable. It may also be helpful to consider how the behaviors you observe compare to the “equilibrium states" xe for this model. You can determine these by solving x. = r(1 –xe)Xe

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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HW #4 problem 3: In this problem, you will investigate changes in the behavior of x, as predicted by the
"logistic" model x+1 = r(1 – x„)Xn caused by changes in the parameter value r or in the “initial" value
xo. Starting with x, = 0.25, look at the behavior of x1, x2, .X50 for r = 2, then for r = 2.25, then forr =
2.5, and so on until r = 4. Where do you see important changes occur? Repeat this for x, = 0.3 and report
where you see the greatest sensitivity to changes in the initial value. Using Excel or some similarly simple
calculation system will make this problem more manageable. It may also be helpful to consider how the
behaviors you observe compare to the “equilibrium states" xe for this model. You can determine these by
solving x, = r(1 – xe)Xe

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I need the next 3 parts pls!
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7. A commercial fishery is estimated to have carrying capacity 40 tons of salmon. Suppose the annual growth rate of total salmon population P (measured in tons) is governed by the logistic equation P' = P(1 – P/40) and initially there are 30 tons of fish. (i) What is the fish population after 1 year? (You may use e 2 2.72.) Suppose that the owner of the fishery decides to harvest h tons of salmon annually at a constant rate. Then (ii) ( What is the differential equation governing the fish population now? (iii) What is the maximun sustainable harvesting rate? (Justification is required.)
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