A team of scientists are studying two species of deer in a park who are competing for the same grass. Let z be the population of Sika deer, and y be the population of White-tailed deer. After observing many interactions between the two species and monitoring population for a handful of cycles, the scientists form the following dynamical system to model future populations: dr r(2.20 – 0.22r - 2.00y) dy v(2.40- 1.00z - 0.20y) dt (a) Find all the fixed points for this system (b) For cach fixed point, find the eigenvalues and cigenvectors of the Jacobian matrix and thus characterise cach fixed point.
A team of scientists are studying two species of deer in a park who are competing for the same grass. Let z be the population of Sika deer, and y be the population of White-tailed deer. After observing many interactions between the two species and monitoring population for a handful of cycles, the scientists form the following dynamical system to model future populations: dr r(2.20 – 0.22r - 2.00y) dy v(2.40- 1.00z - 0.20y) dt (a) Find all the fixed points for this system (b) For cach fixed point, find the eigenvalues and cigenvectors of the Jacobian matrix and thus characterise cach fixed point.
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
100%
Solve b part only in one hour i need and take a thumb up
Transcribed Image Text:3. A team of scientists are studying two species of deer in a park who are competing
for the same grass. Let z be the population of Sika deer, and y be the population
of White-tailed deer. After observing many interactions between the two species
and monitoring population for a handful of cycles, the scientists form the following
dynamical system
model future populations:
dr
- r(2.20 - 0.22r - 2.00y)
P
dy
- v(2.40 -1.00z -0.20y)
(a) Find all the fixed points for this system
(b) For each fixed point, find the eigenvalues and eigenvectors of the Jacobian
matrix and thus characterise cach fixed point.
(c) Plot the phase portrait for this system
(d) Assume the population of X in the absence of Y in the model above, can be
modelled by the logistic model as follows:
dt
What are the values of r and k in this model?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps
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,
