for the same grass. Let z be the population of Sika deer, and y be the population of White-tailed deer. After observing many interactions between the two species and monitoring population for a handful of cycles, the scientists form the following dynamical system to model future populations: dr r(2.20 – 0.22r - 2.00y) dy y(2.40- 1.00r-0.20y) dt (a) Find all the fixed points for this system (b) For each fixed point, find the eigenvalues and eigenvectors of the Jacobian matrix and thus characterise cach fixed point. (c) Plot the phase portrait for this system (d) Assume the population of X in the absence of Y in the model above, can be modelled by the logistic model as follows: 里一

for the same grass. Let z be the population of Sika deer, and y be the population of White-tailed deer. After observing many interactions between the two species and monitoring population for a handful of cycles, the scientists form the following dynamical system to model future populations: dr r(2.20 – 0.22r - 2.00y) dy y(2.40- 1.00r-0.20y) dt (a) Find all the fixed points for this system (b) For each fixed point, find the eigenvalues and eigenvectors of the Jacobian matrix and thus characterise cach fixed point. (c) Plot the phase portrait for this system (d) Assume the population of X in the absence of Y in the model above, can be modelled by the logistic model as follows: 里一

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

See similar textbooks

Similar questions

2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
b) What are the three models proposed as extensions of the GARCH model? Describe their advantages over the GARCH.
It is known that in any given year, • 90% of the people in a city move to the suburbs; • 80% of the people in the suburbs do not move to the city. Given an initial city population of 55,000 and an initial suburb population of 77,000, what are the long-term population levels of the city and the suburb?
1.1 Find the independent nonlinearity and the correlation coefficient for the following set of inputs and outputs from a nearly linear system. Instrument was designed for an output equal to twice the input. Full scale is 20. Input 0.50 1.50 2.00 5.00 10.00 Output 0.90 3.05 4.00 9.90 20.50
The manager of a market can hire either Mary or Alice. Mary, who gives you service at an exponential rate 20 customers per hour, can be hired at a rate of $3 per hour. Alice, who gives service at an exponential rate of 30 customers per hour, can hired at a rate of $C per hour. The manager estimates that, on the average, each customer’s time is worth $1 per hour and should be accounted for in the model. Assume customers arrive at a Poisson rate of 10 per hour. a) What is the average cost per hour if Mary is hired? If Alice is hired? b) Find C if the average cost per hour is the same for Mary and Alice.
Exercise 1.14 (Static) THE BANK CUSTOMER WAITING TIME CASE A bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. Typical waiting times during peak business hours under the current system are roughly 9 to 10 minutes. The bank manager hopes that the new system will lower typical waiting times to less than 6 minutes and wishes to evaluate the new system. When the new system is operating consistently over time, the bank manager decides to select a sample of 100 customers that need teller service during peak business hours. Specifically, for each of 100 peak business hours, the first customer that starts waiting for teller service at or after a randomly selected time during the hour will be chosen. Consider the peak business hours from 2:00 p.m. to 2:59 p.m., from 3:00 p.m. to 3:59 p.m., from 4:00 p.m. to 4:59 p.m., and from 5:00 p.m. to 5:59 p.m. on a particular day. Also, assume that a computer software…