1. Draw the orbit analysis or phase portrait of f(x) = x3 - X. 2. Find...
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)...
please, be explicit 4. Find all fixed points for each of the following maps and classify them as cobweb for the typical trajectories. a) f(x) 2r(1-); b) f(z) -; c) f(z) ; d) f() 4+ attracting, repelling, or neutral. Draw a 4. Find all fixed points for each of the following maps and classify them as cobweb for the typical trajectories. a) f(x) 2r(1-); b) f(z) -; c) f(z) ; d) f() 4+ attracting, repelling, or neutral. Draw a
Let f(x) = 3x − 3x^2 . Show that 2/3 is an attracting fixed point. Graphical analysis is not sufficient.
(1 point) Use the applet provided to draw a phase portrait for ' = -2x(1 - 2)(2-2) The above equation could represent a model of a population that can become extinct if it drops below a particular critical value. What is this critical value? (1 point) Determine the bifurcation value(s) for the one parameter family k = 0 help (numbers) Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your...
Solve the linear svstenm Find the equilibrium and determine its type. Draw the phase portrait showing the eui librium, the ray solutions, and sketch other trajectories showing the direction. Find the solution with the initial conditions x(0) = 1, y(0) = 0.
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...
3. Find all fixed points for the associated Newton iteration function for F(a) z/ 1) when n-1,2,3... Which are attracting and which are repelling? 3. Find all fixed points for the associated Newton iteration function for F(a) z/ 1) when n-1,2,3... Which are attracting and which are repelling?
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.
1 (c) (12 pts) Consider the logistic equation IP 3 Use phase portrait analysis to classify the equilibrium solutions as asymptotically stable, 10 unstable or semi-stable. (ii) Find the general solution to the ODE. (The solution may be expressed in implicit form.) 1 (c) (12 pts) Consider the logistic equation IP 3 Use phase portrait analysis to classify the equilibrium solutions as asymptotically stable, 10 unstable or semi-stable. (ii) Find the general solution to the ODE. (The solution may be...
pls choose the answer like a,b,c,d for these 5 multichoice question don't mind what i choose What can be said about the following differential equation? dy 7t It is autonomous, non-separable, linear and non-homogenous It is non-autonomous, non-separable, linear and non-homogenous It is autonomous, separable, linear and homogenous It is autonomous, separable, linear and non-homogenous. Consider the following differential equation: dt the function FA(x) -22 A, with A0, undergoes a bifurcation. Identify the type of bifurca tion. F has two...