Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
4. Suppose that an insect population, z(t), is controlled by a natural predator population, y(t). a) Write down the Lotka-Volterra predator-prey model that can describe the inter- action of these populations. b) Find and graph the null-clines and the equilibria of your model. Sketch a vector- field in the phase plane. c) Suppose an insecticide is applied, but it is also toxic to the predators. Hence, the poison kills both predator and prey at rates proportional to their respective populations. Modify your model from a) to take this into account, and write out the new model governing the populations.

4. Suppose that an insect population, z(t), is controlled by a natural predator population, y(t). a) Write down the Lotka-Volterra predator-prey model that can describe the inter- action of these populations. b) Find and graph the null-clines and the equilibria of your model. Sketch a vector- field in the phase plane. c) Suppose an insecticide is applied, but it is also toxic to the predators. Hence, the poison kills both predator and prey at rates proportional to their respective populations. Modify your model from a) to take this into account, and write out the new model governing the populations.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
4. Suppose that an insect population, r(t), is controlled by a natural predator population, y(t). a) Write down the Lotka-Volterra predator-prey model that can describe the inter- action of these populations. b) Find and graph the null-clines and the equilibria of your model. Sketch a vector- field in the phase plane. c) Suppose an insecticide is applied, but it is also toxic to the predators. Hence, the poison kills both predator and prey at rates proportional to their respective populations. Modify your model from a) to take this into account, and write out the new model governing the populations. d) Find the equilibria of the new model, and compare them to your results under b). How does the application of the insecticide change the equilibrium levels of the insects and their natural predator? What does this mean?
Transcribed Image Text:4. Suppose that an insect population, r(t), is controlled by a natural predator population, y(t). a) Write down the Lotka-Volterra predator-prey model that can describe the inter- action of these populations. b) Find and graph the null-clines and the equilibria of your model. Sketch a vector- field in the phase plane. c) Suppose an insecticide is applied, but it is also toxic to the predators. Hence, the poison kills both predator and prey at rates proportional to their respective populations. Modify your model from a) to take this into account, and write out the new model governing the populations. d) Find the equilibria of the new model, and compare them to your results under b). How does the application of the insecticide change the equilibrium levels of the insects and their natural predator? What does this mean?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS