For u = 0 we obtain the logistic DE on the line: i= r – r. Draw ihe phase line for this system. Identify and classify the equilibria.
For u = 0 we obtain the logistic DE on the line: i= r – r. Draw ihe phase line for this system. Identify and classify the equilibria.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.4: Solving Nonlinear Equations
Problem 17E: Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law,...
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Question
100%
Just solve part 1 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- H: (1+ sin (t))) – x²
We can also view this equation as an autonomous system on the plane:
(1- H. (1+ sin (
Ô = 1
(0))) – r²
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 = x – x².
Draw the phase line for this system. Identify and classify the equilibria.
1
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5953f1ea-51ea-4b60-957a-f5cac2196f2a%2Fa802a1b5-f08d-49f3-8866-781fb8ce711a%2Fnqacisp_processed.jpeg&w=3840&q=75)
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- H: (1+ sin (t))) – x²
We can also view this equation as an autonomous system on the plane:
(1- H. (1+ sin (
Ô = 1
(0))) – r²
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 = x – x².
Draw the phase line for this system. Identify and classify the equilibria.
1
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.
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