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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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?
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?
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