Find all biologically meaningful steady states

Assignment Help Mathematics
Reference no: EM131068447

Question 1- Find the (2, 2)-entry of the Jacobian matrix of the function

1884_Figure.png

At the point (2, 1).

Question 2- Consider the nonlinear system

x' = 12 - 0.1xy - 0.3

y' = 0.1xy - 2y

in the region x, y ≥ 0

a) Draw the x-and y-nullclines.

b) Identify all equilibria.

c) Sketch the phase portrait.

Question 3- Consider a disease that propagates according to the system

dx/dy = 16 - 0.2xy - 0.4x

dy/dx = 0.1xy - 8y

where x represented susceptible individuals, y represented infected individuals

a) Find all biologically meaningful steady states.

b) Show that the Jacobian matrix of this system is given by

1702_Figure1.png

c) For the biologically meaningful steady from (a), find the eigenvalues of the Jacobian matrix.

d) Determine the stability of the biologically meaningful steady states.

Reference no: EM131068447

Questions Cloud

Directed to employees-emphasizing effective consumer : Create a motivational bulletin of 350 to 700 words that could be posted throughout your workplace, directed to employees, emphasizing effective consumer relations. Include the following:
What consequences did the offender sustain-prison time : Compare white collar crime in the United States to white collar crime in India: what are the characteristics of people in India who commit white collar crime (e.g: age, occupation or profession, lifestyle). Find a case of white collar crime that ..
Firm has issued cumulative preferred stock : A firm has issued cumulative preferred stock with a $100 par value and a 12 percent annual dividend. For the past two years, the board of directors has decided not to pay a dividend. the preferred stockholders must be paid prior to paying the common ..
Transactions involving the short-term securities investments : Prepare journal entries to record the following transactions involving the short-term securities investments of Duke Co., all of which occurred during year 2015.
Find all biologically meaningful steady states : Find all biologically meaningful steady states. For the biologically meaningful steady from (a), find the eigenvalues of the Jacobian matrix. Determine the stability of the biologically meaningful steady states
What is the amount of the firms net fixed assets : The Caughlin Company has a long-term debt ratio of .38 and a current ratio of 1.60. Current liabilities are $940, sales are $6,360, profit margin is 9.7 percent, and ROE is 19.9 percent. What is the amount of the firm’s net fixed assets?
Corporate financial statements-income statement : Explain why an audit of corporate financial statements-Income Statement, Capital Statement, Income Statement, and Statement of Cash Flows-is important to individuals who use those financial statements to make investment decisions and/or lending d..
Assignment on leadership strategies presentation : Taking on the role of a CEO, develop a PowerPoint presentation of approximately 15 slides that explains how you would adapt the Western leadership strategies of either Heifetz and Linsky or Drucker in your approach to managing an international org..
Explain with the use of demand and supply diagrams : New technology has increased the productivity of solar panel producers.

Reviews

Write a Review

 

Mathematics Questions & Answers

  How fast is the height of the pile increasing

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile increasing w..

  At what rate should the cars be rented to produce

A rental car agency rents 190 card per day at a rate of 27 dollars per day. For each one dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income?

  Write a rule to describe the function

An employee receives a weekly salary of $310 and a 4% commision on all sales

  What percentage error would you find after one year

At your initial meeting with your business partners for CellGenTech. If the old model remained, what percentage error would you find after one year in the predicted and actual value?

  Find the independent and dependent variable

Find the independent and dependent variable

  Determine accumulated rate of change using definite integral

Determine accumulated rates of change using definite integral - Explain how this represents an accumulated rate of change in detail

  Description of derivatives and rate of change

A beacon on a lighthouse 2000m away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500m from P?

  Buying a home is the biggest single investment

Buying a home is the biggest single investment or purchase that most individuals make. This project is designed to give you some insight into the home-buying process and the associated costs. Find all the costs associated with buying a home by..

  Find the elevation of point q

Write equations in a, b, and c that will ensure that the track is smooth at the transition points - Find the elevation of point Q to find an equation for L2

  Merger-acquisition and international strategies

Choose two (2) public corporations in an industry with which you are familiar - one (1) that has acquired another company and operates internationally and one (1) that does not have a history of mergers and acquisitions and operates solely within ..

  Determine how long the bus traveled at each rate

A bus traveled at an average rate of 50 miles per hour then reduced its average rate to 40 miles per hour for the rest of the trip. If the 220-mile trip took 5 hours, determine how long the bus traveled at each rate.

  Unbounded self-adjoint operator

Let H be the unbounded self-adjoint operator defined by -d^2/dx^2 (the negative of the second derivative with respect to x) on: D(H) ={f element of L^2 | Integral( |s^2 F f(s)|^2 )ds element of L^2}

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd