Find the conditions for stability of the equilibrium of Nt + 1 = rNt(1 - Nt) -
Question:
Nt + 1 = rNt(1 - Nt) - hNt
for the following values of r. Show that the equilibrium N* is stable when h is set to the value that maximizes the long-term harvest. Graph the updating function and cobweb.
1. r = 2.5, as in the text.
2. r = 1.5, as in Exercise 46.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 83% (6 reviews)
1 The derivative of the updating function is 251 2N ...View the full answer
Answered By
Joseph Mwaura
I have been teaching college students in various subjects for 9 years now. Besides, I have been tutoring online with several tutoring companies from 2010 to date. The 9 years of experience as a tutor has enabled me to develop multiple tutoring skills and see thousands of students excel in their education and in life after school which gives me much pleasure. I have assisted students in essay writing and in doing academic research and this has helped me be well versed with the various writing styles such as APA, MLA, Chicago/ Turabian, Harvard. I am always ready to handle work at any hour and in any way as students specify. In my tutoring journey, excellence has always been my guiding standard.
4.00+
1+ Reviews
10+ Question Solved
Related Book For
Modeling the Dynamics of Life Calculus and Probability for Life Scientists
ISBN: 978-0840064189
3rd edition
Authors: Frederick R. Adler
Question Posted:
Students also viewed these Calculus questions
-
The nonlinear discrete-time dynamical system How does this differ from the model in Exercise 31? Why is the equilibrium smaller? The model describing the dynamics of the concentration of medication...
-
Analyze the stability of the positive equilibrium in the model from Exercise 44 when = 4, the point where the bifurcation occurs. Right at a bifurcation point, the stability theorem fails because...
-
Without setting r and h to particular values, find the equilibrium algebraically. When is the equilibrium stable? A lab is growing and harvesting a culture of valuable bacteria described by the...
-
An amplifier has three cascaded stages of amplification, each having available power gain of 10 dB and noise figure of 3 dB. i) ii) Calculate the noise factor (ratio), and noise figure (dB). If the...
-
Keiras Sports uses the FIFO inventory method. Keiras Sports started December with 9 helmets that cost $56 each. On December 19, Keiras Sports bought 16 helmets at $51 each. On December 28, Keiras...
-
Consider again the data file fred5 used in Example 13.2 and Exercise 13.6. a. Estimate a VAR model for \(\left\{\Delta C_{t}, \Delta Y_{t} ight\}\) with three lags of each variable included. Comment...
-
A quality control department is testing 25 smartphones from a shipment of 300 smartphones. Describe how this test could be done. Then use technology to generate a list of 25 random numbers from 1 to...
-
The AB Partnership pays its only liability (a $100,000 mortgage) on April 1 of the current year and terminates that same day. Alison and Bob were equal partners in the partnership but have...
-
In an electric motor, a coil with 139 turns of radius 1.80 cm can rotate between the poles of a magnet. The magnetic field magnitude is 0.200 T. When the current through the coil is 37.9 mA, what is...
-
Develop a simulation of an elevator that travels between floors 1 and N where N is an input. Time is sequenced in discrete steps starting at 1; at each time step, the elevator may ascend one floor,...
-
Find the maximum harvest from a population following the discrete-time dynamical system Nt + 1 = rNt(1 - Nt) - hNt for the given values of r. a. Find the equilibrium population as a function of h....
-
Calculate the maximum long-term harvest for an alternative model of competition obeying the discrete-time dynamical system Try the following steps for the given values of the parameters r and k. a....
-
Suppose that the following discrete numbers show the integer values of MWTP and MC as depicted in Figure 4.1. Determine the socially efficient rate of output. Show that at any other output level, the...
-
Explain the factors that influence the development of multichannel customer contact strategies.
-
Measurement of websites concerns the recording of key events involving customers using a website. Briefly explain five different types of event.
-
Select a recent campaign from a charity and with reference to their website campaign pages, identify how they should set campaign goals and review effectiveness.
-
More than just an online fashion for 20-somethings, ASOS has pioneered social shopping. Currently one of the most successful online fashion retailers founded in the UK, ASOS offers tens of thousands...
-
Describe what is meant by positioning strategy. How do the market, customer, internal, and competitive analyses relate to positioning strategy?
-
What are the advantages of making presentations via Internet? Can you think of any negatives? Explain?
-
What will be the final value of DI after executing the following piece of code? Execute the instructions dependently one after another. CLD MOU CX,OFOH MOU AX.02874H MOU DI,01000H MOU ES, DI SUB...
-
The figure shows the daily Dow Jones Industrial Average (DJIA) and its 30-day moving average from late July to early November. Use the figure to complete the following. (a) Approximate the absolute...
-
The graph shows the number of workers, W=f (t), still in the workforce per Social Security beneficiary (historically and projected into the future) as a function of time t, in calendar years with...
-
(a) If the total revenue function for a hammer is R=36x-0.01x2, then sale of how many hammers, x, will maximize the total revenue in dollars? Find the maximum revenue. (b) Find the maximum revenue if...
-
A 1-kg ball moving with a velocity of 2 m/s to the right collides with a 2-kg ball moving with a velocity of 4 m/s to the left. The balls collide elastically and scatter at a 45-degree angle to their...
-
Two balls, one with a mass of 2 kg and the other with a mass of 3 kg, collide elastically. After the collision, the 2-kg ball moves to the left with a velocity of 4 m/s and the 3-kg ball moves to the...
-
A 1-kg ball is moving to the right with a velocity of 2 m/s when it collides with a stationary 2-kg ball. After the collision, the 1-kg ball moves to the left with a velocity of 1 m/s. What is the...
Study smarter with the SolutionInn App