Construct a Liapunov function on the form V(x,y) = ax2 + cy2 for the nonlinear system dx dt dy dt...
2. Consider the nonlinear autonomous system of DEs: dx dt dy dt (a) Find all critical points of this system. (Make sure that you have found all of them.) (b) Find the linearization (a linear system) at each critical point. Calculate the eigen- values of the contant coefficient matrix, classify the corresponding critical point, and state its stability.
dx Consider the system 2 - NICO ху 2 22 dy dt = 2y – 1- 2XY dt 2 (a) Identify all critical points of the system. (b) For each critical point, use eigenvalues to classify the critical points according to stability (stable, unstable, asymptotically stable) and type (saddle, proper node, etc).
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt = 3xy − y 3a (5 pts): Find the steady states of the system. 3b (15 pts): Linearize the model about each of the fixed points and determine the type of stability. 3b (15 pts): Draw the phase portrait for this system, including nullclines, flow trajectories, and all fixed points. Problem 2 (25 pts): Two-dimensional linear ODEs For the following linear systems, identify the...
6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) = 4x2 - X2?; f(x) = x/2-44 a. Find the equilibrium points. (5 pts.) b. Find the linearized system around each equilibrium point. (5 pts.) C. Which of these equilibrium points is (are) and what the pole values for the stable equilibrium points? (5 pts.) 6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) = 4x2 - X2?; f(x)...
X Assume X = y Write the linear system in matrix form. 7 dx = X-V z t- 1 dt dy 5xy z 7t2 - dt dz = x dt t2 t 5 z y -1 0 t2 t X + X' = 5 Talk to a Tutor Need Help? Read It 히용 허님 히능
7. Use the Laplace transform to solve the system dx dt -x + y dy = 2x dt x(0) = 0, y(0) = 1
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
Find dy/dt using the given values. y = x - 4x for x = 3, dx/dt = 2. y = [ X dt . dx/dt = 2. Enter an exact number
Solve the system of differential equations dx/dt = x-y, dy/dt = 2x+y subject to the initial conditions x(0)= 0 and y(0) = 1.
In Problems 3-6, find the critical point set for the given system. dx 4. dx = x-y, 3. dt y1 dt dy dy = x2 y2 - 1 dt = x + y + 5 dt dx dx x2- 2xy y2- 3y 2 6. 5. dt dt dy dy 3xy - y2 (x- 1)(y 2) dt dt