Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
For u = 0 the (r, 0) system becomes decoupled. Identify all periodic solutions and explain if they are stable or unstable. 2.

For u = 0 the (r, 0) system becomes decoupled. Identify all periodic solutions and explain if they are stable or unstable. 2.

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
100%
2) kindly solve part 2 correctly and handwritten
7:55 "Z O l O 17% Let's put everything together! What happens when we take a logistic model for population growth and make the carrying-capacity depend on time? (1-4· (1+ sin (t))) – x² i =r We can also view this equation as an autonomous system on the plane: (1- H. (1+ sin ( (0))) – r² i =r 0 = 1 Using the methods we developed in class, we can analyze the behavior one piece at a time! Note: There are two pages. For u = 0 we obtain the logistic DE on the line: i = r – r². Draw the phase line for this system. Identify and classify the equilibria. 2. For u = 0 the (r, 0) system becomes decoupled. Identify all periodic solutions and explain if they are stable or unstable. For 0 < µ < and e > 0 sufficiently small, consider the closed and bounded "washer" region of the plane given by e <r < 1 and 0 <0< 2n. Show that solutions that start in this region stay in this region for all time and explain why this means that a closed orbit exists. 3. Explain why using the linearization theorem on the (r, 0) system will NOT help us determine the stability of any fixed points. 4.
Transcribed Image Text:7:55 "Z O l O 17% Let's put everything together! What happens when we take a logistic model for population growth and make the carrying-capacity depend on time? (1-4· (1+ sin (t))) – x² i =r We can also view this equation as an autonomous system on the plane: (1- H. (1+ sin ( (0))) – r² i =r 0 = 1 Using the methods we developed in class, we can analyze the behavior one piece at a time! Note: There are two pages. For u = 0 we obtain the logistic DE on the line: i = r – r². Draw the phase line for this system. Identify and classify the equilibria. 2. For u = 0 the (r, 0) system becomes decoupled. Identify all periodic solutions and explain if they are stable or unstable. For 0 < µ < and e > 0 sufficiently small, consider the closed and bounded "washer" region of the plane given by e <r < 1 and 0 <0< 2n. Show that solutions that start in this region stay in this region for all time and explain why this means that a closed orbit exists. 3. Explain why using the linearization theorem on the (r, 0) system will NOT help us determine the stability of any fixed points. 4.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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