Question

Sunfish (S) and trout (T) both live in a lake. As they both compete for the same food sources, their populations S and T respectively satisfy $\frac{dS}{dt} = 2S(8-S-2T)$ $\frac{dT}{dt} = T(9-3S-T)$. (a) Find and classify all critical points of this system. You should find the eigenvalues for all of the equilibrium solutions and the eigenvectors for all of them except the one where both S and T are non-zero. You want to classify this point, but do not need the eigenvectors. (b) Sketch out a phase portrait for this system, marking all critical points with their eigen- vectors and direction of flow. (c) Determine what will happen to the population of both species of fish over time. Does this depend on the initial condition? Secondly, consider a different lake and food source where the populations satify the equations $\frac{dS}{dt} = S(10-3S-T)$ $\frac{dT}{dt} = T(7-S-4T)$. Answer the same parts above for this new system.

Name: sunfish s and trout t both live in a lake as they both compete for the same food sources their populations s and t respectively satisfy fracdsdt 2s8 s 2t fracdtdt t9 3s t a find and classify 65189
Uploaded: 2024-07-17T12:40:30-08:00
Duration: 8 min 13 s
Channel: Sam Stansfield
Description: sunfish s and trout t both live in a lake as they both compete for the same food sources their populations s and t respectively satisfy fracdsdt 2s8 s 2t fracdtdt t9 3s t a find and classify 65189

          Sunfish (S) and trout (T) both live in a lake. As they both compete for the same food sources,
their populations S and T respectively satisfy
$\frac{dS}{dt} = 2S(8-S-2T)$
$\frac{dT}{dt} = T(9-3S-T)$.
(a) Find and classify all critical points of this system. You should find the eigenvalues for all
of the equilibrium solutions and the eigenvectors for all of them except the one where both
S and T are non-zero. You want to classify this point, but do not need the eigenvectors.
(b) Sketch out a phase portrait for this system, marking all critical points with their eigen-
vectors and direction of flow.
(c) Determine what will happen to the population of both species of fish over time. Does this
depend on the initial condition?
Secondly, consider a different lake and food source where the populations satify the equations
$\frac{dS}{dt} = S(10-3S-T)$
$\frac{dT}{dt} = T(7-S-4T)$.
Answer the same parts above for this new system.

$sunfish s and trout t both live in a lake as they both compete for the same food sources their populations s and t respectively satisfy fracdsdt 2s8 s 2t fracdtdt t9 3s t a find and classify 65189$

Added by Rosario B.

Question

Please give Ace some feedback