90. Sustainable Harvesting Suppose that a fish population evolves according to the logistic equation and that a fixed num- ber of fish per unit time are removed. That is, (1-2) dN = rN dt N - H K Assume that r = 2 and K = 1000. %3D (a) Find possible equilibria, and discuss their stability when H = 100. (b) What is the maximal harvesting rate that maintains a positive population size?
90. Sustainable Harvesting Suppose that a fish population evolves according to the logistic equation and that a fixed num- ber of fish per unit time are removed. That is, (1-2) dN = rN dt N - H K Assume that r = 2 and K = 1000. %3D (a) Find possible equilibria, and discuss their stability when H = 100. (b) What is the maximal harvesting rate that maintains a positive population size?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![90. Sustainable Harvesting Suppose that a fish population
evolves according to the logistic equation and that a fixed num-
ber of fish per unit time are removed. That is,
dN
N
*(1-*)-
rN
dt
K
Assume that r=2 and K = 1000.
%3D
(a) Find possible equilibria, and discuss their stability when
H = 100.
%3D
(b) What is the maximal harvesting rate that maintains a positive
population size?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2921ecad-2ea4-4a45-ab8d-a94f7a357800%2F7b501054-42e8-41f0-92cc-280245860f0c%2Felhgdk8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:90. Sustainable Harvesting Suppose that a fish population
evolves according to the logistic equation and that a fixed num-
ber of fish per unit time are removed. That is,
dN
N
*(1-*)-
rN
dt
K
Assume that r=2 and K = 1000.
%3D
(a) Find possible equilibria, and discuss their stability when
H = 100.
%3D
(b) What is the maximal harvesting rate that maintains a positive
population size?
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