1. The logistic equation is a classical model of population growth and is given by dx(1) = x(1) (1 – x6)). dt In the logistic equation, the model parameter K > 0 represents the carrying capacity of the population x(t). First, plot ƒ(x) = x(1) (1-x(7)) K as a function of x to find the equilibrium solutions of the logistic equation. Next, determine which of the equilibrium solutions are attracting. Finally, consider a population y(t) that satisfies the logistic equation with an additional death rate d. The population y satisfies dy(t) = y(1) (1 – ³()) – dy(t). K Find the equilibrium of this new model and determine the maximal value of d that allows for long-term population persistence (i.e. no extinction).
1. The logistic equation is a classical model of population growth and is given by dx(1) = x(1) (1 – x6)). dt In the logistic equation, the model parameter K > 0 represents the carrying capacity of the population x(t). First, plot ƒ(x) = x(1) (1-x(7)) K as a function of x to find the equilibrium solutions of the logistic equation. Next, determine which of the equilibrium solutions are attracting. Finally, consider a population y(t) that satisfies the logistic equation with an additional death rate d. The population y satisfies dy(t) = y(1) (1 – ³()) – dy(t). K Find the equilibrium of this new model and determine the maximal value of d that allows for long-term population persistence (i.e. no extinction).
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
Transcribed Image Text:1. The logistic equation is a classical model of population growth and is given by
d
= (x(1) = x(1) (1 − x()).
dt
K
In the logistic equation, the model parameter K > 0 represents the carrying capacity of
the population x(t). First, plot
ƒ(x) = x(1) (1 — x(0))
K
as a function of x to find the equilibrium solutions of the logistic equation. Next, determine
which of the equilibrium solutions are attracting.
Finally, consider a population y(t) that satisfies the logistic equation with an additional
death rate d. The population y satisfies
d
{y(t) = y(t)(1 – x(t)) –
(t)) - dy(t).
Find the equilibrium of this new model and determine the maximal value of d that allows
for long-term population persistence (i.e. no extinction).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 13 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
