Exercise 5. (Fishery Model) The equation N = rN(1 –) – H represent a simple population model of a fishery with the term –H representing a constant harvesting rate (H > 0). a) Show that the system can be written in dimensionless form as dr = ¤(1–¤) – h dr for suitably defined dimensionless quantities.
Exercise 5. (Fishery Model) The equation N = rN(1 –) – H represent a simple population model of a fishery with the term –H representing a constant harvesting rate (H > 0). a) Show that the system can be written in dimensionless form as dr = ¤(1–¤) – h dr for suitably defined dimensionless quantities.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Exercise 5.
(Fishery Model) The equation N = rN(1 – ) – H represent a
K
simple population model of a fishery with the term -H representing a constant harvesting
rate (H > 0).
a) Show that the system can be written in dimensionless form as
dx
= #(1–2) – h
dT
for suitably defined dimensionless quantities.
b) Plot the vector fields for different values of h (show all qualitative behaviors).
c) Show that a bifurcation happens at a critical value he, determine the value, and classify
the bifurcation.
d) Discuss the long-time behavior of the population for h < he and h > he, and give a
biological interpretation to both cases.
e)
have explored. Determine what the flaw is and advance a possible solution. (Hint: it is
related to a missing fixed point)
This model has a major flaw compared to other population models we](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b0185de-0645-4c2a-aea4-e046d61ab5cb%2F8dd83eb2-2cd7-4927-ab14-abf0f81ca1bf%2Fuau24p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 5.
(Fishery Model) The equation N = rN(1 – ) – H represent a
K
simple population model of a fishery with the term -H representing a constant harvesting
rate (H > 0).
a) Show that the system can be written in dimensionless form as
dx
= #(1–2) – h
dT
for suitably defined dimensionless quantities.
b) Plot the vector fields for different values of h (show all qualitative behaviors).
c) Show that a bifurcation happens at a critical value he, determine the value, and classify
the bifurcation.
d) Discuss the long-time behavior of the population for h < he and h > he, and give a
biological interpretation to both cases.
e)
have explored. Determine what the flaw is and advance a possible solution. (Hint: it is
related to a missing fixed point)
This model has a major flaw compared to other population models we
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)