A population of deer live in a forest. They have no natural predator, and are limited...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A population of deer live in a forest. They have no natural predator, and are limited only by the resources available to them. (a) The deer population p(t) is governed by the logistic growth equation dp (1-P), dt where r is the growth rate and N is the population carrying capacity. The time variable t is measured in months. (i) If this system is dimensionally consistent, what are the units of r? What does the quantity r mean? =rp (ii) Set r= 0.25, N = 20000, and p(0) = 1000 + 10008, where ß is the third digit of your MQ student number. Use ode45 to simulate the population over a 15 year period. (b) A nearby village decides to hunt deer in a way that allows the population to be sustainable. They hunt seasonally, so that deer have time to recover after each hunting season. The deer equation is now governed by dp dt = rp 1+ sin 2 (i) Use the same parameters as in the previous question. Set a = 200 and use ode45 to simulate the population over a 15 year period. 2πt (ii) How large a value can a take while allowing the deer to reach a sustainable population. What happens if a exceeds this value? Support your answer with example simulations. (iii) Is there a way the villagers could adapt their behaviour to so they can choose larger values of a than the critical value from (ii)? Show this using an example simulation. An overdamped bead on a rotating ring has the following dimensional equation: de fl = -mg sin 0 + mrw² sin 0 cos 0. dt de dT Here, 0(t) is the angle of the bead, where angle is a dimensionless quantity in the range 0 € (-, T]. The mass of the bead is m and the radius of the ring is r. The ring rotates around. its vertical axis with a constant angular velocity (radians/unit time) of w. The value is the damping coefficient. All constants are positive. (a) If this expression is dimensionally consistent, what are the dimensions of μ? (b) By appropriately non-dimensionalizing this equation, obtain = sin 0(k cos 01). (c) What are the critical points of this model for k = 1/2, k = 1, and k = 2? Sketch the phase lines for each case. (d) Using the linear stability criterion, determine the stability of the critical points in the model for k= 1/2 and k = 2. What happens if you try to apply this criterion to the k = 1 case? (e) Show that k = 1 is the bifurcation value. What does this tell us about the required rotational angular velocity required for the bead to settle at a nonzero angle? How does it change if we use a ring with a larger radius? (f) Plot the bifurcation diagram for this model. A population of deer live in a forest. They have no natural predator, and are limited only by the resources available to them. (a) The deer population p(t) is governed by the logistic growth equation dp (1-P), dt where r is the growth rate and N is the population carrying capacity. The time variable t is measured in months. (i) If this system is dimensionally consistent, what are the units of r? What does the quantity r mean? =rp (ii) Set r= 0.25, N = 20000, and p(0) = 1000 + 10008, where ß is the third digit of your MQ student number. Use ode45 to simulate the population over a 15 year period. (b) A nearby village decides to hunt deer in a way that allows the population to be sustainable. They hunt seasonally, so that deer have time to recover after each hunting season. The deer equation is now governed by dp dt = rp 1+ sin 2 (i) Use the same parameters as in the previous question. Set a = 200 and use ode45 to simulate the population over a 15 year period. 2πt (ii) How large a value can a take while allowing the deer to reach a sustainable population. What happens if a exceeds this value? Support your answer with example simulations. (iii) Is there a way the villagers could adapt their behaviour to so they can choose larger values of a than the critical value from (ii)? Show this using an example simulation. An overdamped bead on a rotating ring has the following dimensional equation: de fl = -mg sin 0 + mrw² sin 0 cos 0. dt de dT Here, 0(t) is the angle of the bead, where angle is a dimensionless quantity in the range 0 € (-, T]. The mass of the bead is m and the radius of the ring is r. The ring rotates around. its vertical axis with a constant angular velocity (radians/unit time) of w. The value is the damping coefficient. All constants are positive. (a) If this expression is dimensionally consistent, what are the dimensions of μ? (b) By appropriately non-dimensionalizing this equation, obtain = sin 0(k cos 01). (c) What are the critical points of this model for k = 1/2, k = 1, and k = 2? Sketch the phase lines for each case. (d) Using the linear stability criterion, determine the stability of the critical points in the model for k= 1/2 and k = 2. What happens if you try to apply this criterion to the k = 1 case? (e) Show that k = 1 is the bifurcation value. What does this tell us about the required rotational angular velocity required for the bead to settle at a nonzero angle? How does it change if we use a ring with a larger radius? (f) Plot the bifurcation diagram for this model.
Expert Answer:
Answer rating: 100% (QA)
a i To determine the units of r lets analyze the logistic growth equation dpdt rp1 pN The lefthand side represents the rate of change of the population with respect to time which has units of populati... View the full answer
Related Book For
Essentials of Marketing Research
ISBN: 978-1305263475
6th edition
Authors: Barry J. Babin, William G. Zikmund
Posted Date:
Students also viewed these accounting questions
-
What are some pros and cons to 360-degree feedback?
-
What are the pros and cons to BMWs selective target marketing? What has the firm done well over the years and where could it improve?
-
What are pros and cons of using M-Turk crowd sourcing to provide a sample for a marketing research study? Would you advise someone trying to predict which type of appeals for energy efficient...
-
Consider the deletion of record 5 from the file as shown below compare the relative merits of the following techniques for implementing the deletion: a. Move record 6 to the space occupied by record...
-
Consider again the conditions of Exercise 3, including the observations in the random sample of 128 families, but suppose now that it is desired to test the composite null hypothesis H0 that the...
-
What is the advantage of using frames when displaying information on the Internet?
-
Identify the two ways that trial material may be organized. What are the advantages and disadvantages of each method?
-
In each of the following independent situations, indicate whether the alternate valuation date can be elected. Explain why or why not. All deaths occur in 2015. Value of Gross Estate Estate Tax...
-
Green Valley Company prepared the following trial balance at the end of its first year of operations ending December 31. To simplify the case, the amounts given are in thousands of dollars. Cash...
-
Calculator Calculating Payroll Taxes Expense and Preparing Journal Entry Selected information from the payroll register of Ebeling's Dairy for the week ended July 7, 20--, is shown below. The SUTA...
-
Keaubie Co. issued $280,000, 10%, 10-year bonds payable at a price of 95, on Jan. 1, 2019 a. Journalize the issuance of the bonds b. Journalize the first semi-annual interest payment and amortization...
-
Sandhill Inc. sells prepaid telephone cards to customers in its convenience stores. When Sandhill sells cards, it then pays the telecommunications company, Blossom, for the value of the cards less a...
-
On December 31, 2024, the end of the fiscal year, California Microtech Corporation held its semiconductor business for sale at year- end. The estimated fair value of the segment's assets, less costs...
-
Can you determine whether the below actions ( i ) to ( v ) can be categorized as a ) Tax Planning, b ) Tax Management, orc ) Tax Evasion, providing reasons for eachi. Mr . Sarthak deposits 1 , 2 5 ,...
-
According to the text the importance of communication is illustrated by the example of the experiment of German Emperor, Frederick II, which had very serious effects. According to the text, what are...
-
After the formation of RGM Partnership on July 4 , 2 0 2 3 , the balances in the general ledger accounts reflect the following balances: Debit Credit Cash P 2 0 5 , 0 0 0 Accounts Receivable 9 5 , 0...
-
What strategies can be employed to transform poorly formulated questions into effective ones that promote constructive dialogue and deeper inquiry?
-
Design an experiment to demonstrate that RNA transcripts are synthesized in the nucleus of eukaryotes and are subsequently transported to the cytoplasm.
-
What are the advantages of using a slider scale?
-
In each of the following, identify the type of scale and evaluate it: a. A U.S. representatives questionnaire sent to constituents: Do you favor or oppose the Fair Tax Proposal? b. How favorable are...
-
What are four questions researchers can ask in deciding whether their electronic data gathering systems violate good ethical principles?
-
Following is a probability density curve with the area between 0 and 1 and the area between 1 and 2 indicated. a. What proportion of the population is between 0 and 1? b. What is the probability that...
-
Use Table A.2 to find the area between z = 1.13 and z = 2.02. Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -0.8 -0.7 .2119 .2090 .2420 2389 -0.6 .2743 .2709 .2676 .2061 .2033 2358 .2327 .2643...
-
Use Table A.2 to find the area to the left of z = 0.25. Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -0.8 -0.7 .2119 .2090 .2420 2389 -0.6 .2743 .2709 .2676 .2061 .2033 2358 .2327 .2643 .2005...
Study smarter with the SolutionInn App