Solve the linear svstenm Find the equilibrium and determine its type. Draw the phase portrait showing...
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutions and determine their type (e.g., spiral source, saddle) Hint: you should find three equilibria. b) For each of the equilibria you found in part (a), draw a phase portrait showing the behaviour of solutions near that equilibrium. -2 (c) Find the nullclines for the system and sketch them on the answer sheet provided. Show the direction of the vector field...
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field. Use the points: (0,0), (+1,0), (0, +1), (+1, +1). (b) Draw the phase portrait. (c) Classify the equilibrium solution with its stability. 11 and 2. Suppose 2 x 2 matrix A has eigenvalues – 3 and -1 with eigenvectors respectively. (a) Find the general solution of 7' = A. (b) Draw the phase portrait. (C) Classify the equilibrium solution with its stability. 3. Suppose...
dx/dt = 4x -x^2 -2xy dy/dt = -y+0.5 xy a) find equilibrium points b) find Jacobian matrix for above system c) find Jacobian matrix at eq. point (0,0) d) draw phase portrait near (0,0) from © e) show at eq. point (4,0) the Jacobian matrix is -4 -8 0 1 f) draw phase portrait near (4,0) from (d) g) at eq. point (2,1) the Jacobian matrix is -2 -4 0.5 0 h) draw phase portrait near (2,1) from (f) i)...
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Classify the equilibrium (b) If λί is the eigenvalue with corresponding eigenvector (1,1) and A2 is the eigenvalue with corresponding eigenvector (-1,3), place the three numbers 0, λ, and λ2 in order frorn least to greatest. (c) If ((t), y(t) is the solution satisfying the initial condition (x(0),y(0)- (-2,2). Find i. lim r(t) i. lim rlt) ii. lim y(t) iv. lim y(t)
Here is...
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine the type of the equilibrium point at the origin. (35 points) (b) Find all straight-line solutions and draw the phase portrait for the system. (35 points) (c) What is the general solution to the system? (15 points) (d) Find the solution of the system with initial conditions: x(0) = 1 and y(0) = -1. (15 points)
Please show all work and answer
ASAP!!
5) Consider the epidemic model x' = -3.cy -0.5.0 + 0.5 y' = 3.cy - 1.5y Find all the equilibrium points and determine their type and stability type. Show the equilibrium points on the (x,y)-plane and sketch the phase portrait near each equilibrium showing the direction of trajectories. For saddles/nodes show the eigenvectors; for spirals determine the direction of rotation.
1) Find the general solution of di = Ay where Then sketch the phase portrait in the x-y plane, where Finally, classify the equilibrium solution at the origin as a source, spiral sink, etc. 2) Repeat for the matrix | 3 -31 -2 -2] 3) Repeat for the matrix 4 — 4) Repeat for the matrix [95 -9 15 but you don't need to sketch the phase portrait.
Classify the critical point (0, 0) of the given linear system. Draw a phase portrait. dx/df 3x+ y a. dx/dt -x+ 2y dx/dt =-x +3y dy/dt -2x + y dy/dt x+ y Classify the stationary point (0, 0) of the given linear system. Draw a phase portrait. dy/dt -x+y b. dx/dt =-2x-y dx/dt-2x +5/7 y dx/dt 3x-y dx/dt 3x dy/dt 3x- y dy/dt 7x- 3y dy/dt x+y dy/dt 3y
Consider the following system:
dx/dt=y(x^2+y^2-1)
dy/dt= -x(x^2 +y^2-1)
Find the equilibrium solution.
13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of
13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...