3. Suppose x, y, z satisfy the competing species equations 2(6 - 2x - 3y -...
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 <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >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 (2,0,0) is stable, where I > 0.
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)...
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
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)...
pls solve these three parts of the question a) Show that the vector + =(x+2y+4z)i +(2x-3y-z)j +(4x-y-22). is irrotational and find its 7 scalar potential. b) Find the directional derivative of xyz + xz at (1, 1, 1) in a direction of the normal to the 171 surface 3xy? + y= z at (0, 1, 1). c) Find the angle between the normal to the surface x2 = yz at the points (1, 1, 1) and (2, 4, 1). (6)
Please complete #3. 2. Let f(x,y,z 3x2 + 4y2 +5z2- xy - xz - 2zy +2x -3y +5z. Apply 20 steps of Euler's method with a step size of h 0.1 to the system x'(t) y(t)Vf(x(t), y(t), z(t)) z'(t) (x(0), y(0), z(0)) = (-0.505-08) to approximate a point where the minimum of f occurs. Give the value of x (2) (which is the x coordinate of the approximate point where the minimum occurs). Note: This process is called the modified...
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 =
1. The populations of two competing species x(t) and y(t) are governed by the non-linear system of differential equations dx dt 10x – x2 – 2xy, dy dt 5Y – 3y2 + xy. (a) Determine all of the critical points for the population model. (b) Determine the linearised system for each critical point in part (a) and discuss whether it can be used to approximate the behaviour of the non-linear system. (c) For the critical point at the origin: (i)...