In Problems 11 and 12, we consider the effect of modifying the equation for the prey
Consider the system
Where
a) Find all critical points of the given system. How does their location change as
b) Determine the nature and stability characteristics of each critical point.
c) Show that there is a value of
d) Describe the effect on the two population as
Trending nowThis is a popular solution!
Chapter 7 Solutions
Differential Equations: An Introduction to Modern Methods and Applications
Additional Math Textbook Solutions
Calculus Volume 3
Thinking Mathematically (6th Edition)
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Mathematical Ideas (13th Edition) - Standalone book
- In each of Problems 5 and 6 the coefficient matrix has a zero eigenvalue. As a result, the pattern of trajectories is different from those in the examples in the text. For each system: Ga. Draw a direction field. b. Find the general solution of the given system of equations. G c. Draw a few of the trajectories. 4 -3 8 -6 5. x' = Xarrow_forwardProblem 2 Suppose the economy of an island behaves as the Solow model (Y=AK1/2L1/2), version 1.0 (constant population). Suppose that the productivity parameter is A=90, the depreciation rate is d=1/10, the savings (investment) rate is s=0.10, and the labor force is equal to 2 million (and constant over time). Suppose in year 2010 the economy is in a steady state. Compute the 2010 values for overall capital (K) and income per worker (Y/L). Pick the closest values. The stock of capital is between 6 and 7 million. Income per worker is between 2.5 and 3.3. O None of the other options The stock of capital is between 62 and 66 trillion. Income per worker is between 16000 and 17000. The stock of capital is between 12md 14 billion. Income per worker is between 4000 and 5000.arrow_forward2. Thermistors measure temperature, have a nonlinear output and are valued for a limited range. So when a thermistor is manufactured, the manufacturer supplies a resistance vs. temperature curve. An accurate representation of the curve is generally given by = a₁ + a₂ ln(R) + a₂ {ln (R)}² + a₂ {ln (R)}³ where T is temperature in Kelvin, R is resistance in ohms, and a 9₁, 9₂, a are constants of the calibration curve. Given the following for a thermistor R T ohm °C 1101.0 25.115 911.S 30.151 656.0 40.120 451.1 50.128 Approximate the value of temperature in °C for a measured resistance of 900 ohms. (Use any method)arrow_forward
- Consider the dynamical system Yk=1 = log (yk) + Yk- Which of the following statements is true about the dynamical system? O The dynamical system has infinite fixed points. The dynamical system has only one fixed points. The dynamical system has.no fixed points.arrow_forwardProblem 20. For the four points b= 0, 8, 8, 20 and t = 0, 1,3,4, we want to find the closest parabola b=C+ Dt +Et². Write the equations Ax=b in the three unknowns x = (C,D,E). Set up the three normal equations AT A = AT b. You do not need to solve the system.arrow_forwardThis is System Modeling & Simulation questionarrow_forward
- An energy company uses three different processes for generating electricity. One of the processes uses wind energy (and so requires no fuel), while the other two consume a combination of biofuel and natural gas. Each process also requires some amount of labour and emits some amount of carbon dioxide. The amount of biofuel (in Mg) and natural gas (in mcf = mega cubic feet) consumed, the labour required (in person-hours), the carbon dioxide (CO₂) emitted (in Mg), and the power generated (in MWh) per day of operation of each process is as follows: Electricity Process generated 20 32 85 1 2 3 CO₂ Labour produced required 0 20 12 13 29 18 Biofuel required 0 10 30 Natural gas required 0 15 40 Each MWh of electricity can be sold at £144 and there is no limit on the amount that can be sold. Over its next planning period, the company has 320 person-hours for labour, 75 Mg of biofuel, and 90 mcf of natural gas available.arrow_forwardAn energy company uses three different processes for generating electricity. One of the processes uses wind energy (and so requires no fuel), while the other two consume a combination of biofuel and natural gas. Each process also requires some amount of labour and emits some amount of carbon dioxide. The amount of biofuel (in Mg) and natural gas (in mcf = mega cubic feet) consumed, the labour required (in person-hours), the carbon dioxide (CO₂) emitted (in Mg), and the power generated (in MWh) per day of operation of each process is as follows: Process 1 2 3 Electricity generated 20 32 85 CO₂ produced 0 12 29 Labour Biofuel required required 20 0 13 10 18 30 Natural gas required 0 15 40 Each MWh of electricity can be sold at £144 and there is no limit on the amount that can be sold. Over its next planning period, the company has 320 person-hours for labour, 75 Mg of biofuel, and 90 mcf of natural gas available. (a) The company emits all the CO₂ it produces into the atmosphere. Due to…arrow_forwardConsider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₁(t) and x₂(t) of salt in tanks A and B, respectively, at time t. dx₁1 dt dx1 dt pure water 3 gal/min mixture 4 gal/min This system is described by the system of equations 1 50 2 25 dx2 dt 2 25 2 25*1 1 + -X2 mixture 1 gal/min -X2 B with initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, instead of pure water, a brine solution containing 3 pounds of salt per gallon is pumped into tank A? -2 25*1 + 50x2+6× dx2 2 - (25)*₁- (25)×₂2 - = x2 dt…arrow_forward
- Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₁(t) and x₂(t) of salt in tanks A and B, respectively, at time t. dx₁ dt dx₂ dt mixture 4 gal/min This system is described by the system of equations 1 50 2 2 25 2 dx₁ dt dx2 dt = = pure water 3 gal/min = 2 25 2 110 25 A + 1 1 mixture 1 gal/min B with initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, instead of pure water, a brine solution containing 4 pounds of salt per gallon is pumped into tank A? mixture 3 gal/minarrow_forwardPlease answer question 10 (see attached document)arrow_forwardThe management of hartman rent a car has allocated $1.5 million to buy a new fleet of automobiles consisting of compact intermediate size cars an full size cars. Compact costs $12000 each intermediate size cars cost $18000 each and full sized cars cost $24000 each.If hartman purchases twice as many compacts as intermediate size cars and the total amount of cars to be purchased is 100, determine how many cars of each type will be used. Solve the problem using gaussian eliminationarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning