figure of nullclines in yz-plane, is drawn below
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7...
3. Suppose x, y, z satisfy the competing species equations 2(6 - 2x - 3y - 2) y(7 - 2.0 - 3y - 22) z(5 – 2x - y -22) (a) (6 points) Find the critical point (0, yc, ze) where yc, ze >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (1,0,0) is stable, where 8c > 0.
3. Suppose x, y, z satisfy the competing species equations 2(6 - 2x - 3y - 2) y(7 - 2.0 - 3y - 22) z(5 – 2x - y -22) (a) (6 points) Find the critical point (0, yc, ze) where yc, ze >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (1,0,0) is stable, where 8c > 0.
2x + 3y < 6 Minimize the quantity z = 2.0 + 3y subject to the constraints < 2 VI ALAI >
1. Let x and y represent two animal populations which satisfy (9-1-3y) y(-6 + 2x) (a) (5 points) What is the relationship between x and y? How does a grow in the absence of y? How does y grow in the absence of x? (b) (5 points) Sketch the nullclines and direction arrows of the system. (c) (4 points) Find the eigenvalues of the interior critical point. (d) (7 points) Sketch the general solution. Be detailed. (e) (4 points) Sketch...
1. Let x and y represent two animal populations which satisfy 2(9- 2 - 3y) y(-6 + 2x) (a) (5 points) What is the relationship between 2 and y? How does a grow in the absence of y? How does y grow in the absence of x? (b) (5 points) Sketch the nullclines and direction arrows of the system. (c) (4 points) Find the eigenvalues of the interior critical point. (d) (7 points) Sketch the general solution. Be detailed. (e)...
7. The vector field F =< 3x2z In y + ze+2 +20, - 3y?, x° In y + ce2 +423 > is conservative. Find a potential function f(x, y, z) such that F=Vf. Y
x + y + z = 6 2x - y - z=-3 3y - 2z = 0 Question 1 (3 points) 1. X = 3. z = Blank 1: Blank 2: Blank 3: Question 2 (2 points) Picture or screenshot of your answer to #1 (from the matrix calculator). BIU E SÅ S T 2
Maximize P = 4x + 5y subject to 2x + y < 50 2 + 3y < 75 2 > 0 y > 0 Identify the feasible region as bounded or unbounded: List the corner points of the feasible region, separated by a comma and a space. If the region is unbounded, create appropriate ghost points and list those as well. For each corner point, list the value of the objective function at that point. The format should be (x1,y1)...
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...
QUESTION 3 Given the following equations: 2x + 3y + z = 13 3x – 4y + 2z=3 x + y + z = 6 Determine x, y, and z. X = , y = and z =