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please, be explicit and use graphs 3. List all periodic points for each of the following...
please, be explicit 4. Find all fixed points for each of the following maps and classify...
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
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...
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...
Please note that all the steps are meant to help solve the problem. Question A1: We have yet to discover what happens wh...
Please note that all the steps
are meant to help solve the problem.
Question A1: We have yet to discover what happens when the matrix that defines our system has a repeated real eigenvalue. Let's start with the case of a system defined by a diagonal matrix, which has the twice repeated real eigenvalue A 3. Follow the steps below to analyze the shape of the trajectories and draw the phase plane portrait: 1. Write down the explicit solution to...
Please show all work and answer ASAP!! 5) Consider the epidemic model x' = -3.cy -0.5.0...
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.
Please answer question 2. Introduction to Trees Thank you 1. Graphs (11 points) (1) (3 points)...
Please answer question 2. Introduction to Trees
Thank you
1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
E and classify all the equilibriun points of each of the folowing nonlmear systems, given that th...
e and classify all the equilibriun points of each of the folowing nonlmear systems, given that the second system is Hamiltonian (aka con- servative). Sketch a phase portrait of each system. di = y(1-x2) dt
e and classify all the equilibriun points of each of the folowing nonlmear systems, given that the second system is Hamiltonian (aka con- servative). Sketch a phase portrait of each system. di = y(1-x2) dt
Exercise 3. (22 pts.) (Rabbits vs. Sheep) a)For each of the following ”rabbits vs. sheep” problems...
Exercise 3. (22 pts.) (Rabbits vs. Sheep) a)For each of the following ”rabbits vs. sheep” problems with x, y ≥ 0. Find the fixed points, classify them (type and stability), and find the eigenvalues and eigenvectors. Then sketch (by hand) a plausible phase portrait indicating nullclines, all relevant trajectories, and indicate all the different basins of attraction. Finally interpret the behavior of the population of the rabbits and sheep for the different systems (compare the three systems) • x˙ =...
1 Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b)...
1
Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b) find the linearization at each critical point and determine the type and stability of each critical point (c) draw a phase portrait confirming the type and stability of all critical points (1) / - (2+)(y-*) V = (4-1)y + r) (2) 1-1- (4) 2 - 1 - ry (5) x = (1-1-y) V-(3--20) Bonus computational work (use technology!) 1. Uee pplane to plot the...
Consider the system: x' = y(1 + 2x) y' = x + x2 - y2 a. Find all the equilibrium points, and lin...
Consider the system: x' = y(1 + 2x) y' = x + x2 - y2 a. Find all the equilibrium points, and linearize the system about each equilibrium point to find the type of the equilibrium point. b. Show that the system is a gradient system, and conclude that it has no periodic solutions. c. Sketch the phase portrait. Explain how you determined what the phase portrait looks like.
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
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
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...
Please note that all the steps
are meant to help solve the problem.
Question A1: We have yet to discover what happens when the matrix that defines our system has a repeated real eigenvalue. Let's start with the case of a system defined by a diagonal matrix, which has the twice repeated real eigenvalue A 3. Follow the steps below to analyze the shape of the trajectories and draw the phase plane portrait: 1. Write down the explicit solution to...
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.
Please answer question 2. Introduction to Trees
Thank you
1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
e and classify all the equilibriun points of each of the folowing nonlmear systems, given that the second system is Hamiltonian (aka con- servative). Sketch a phase portrait of each system. di = y(1-x2) dt
e and classify all the equilibriun points of each of the folowing nonlmear systems, given that the second system is Hamiltonian (aka con- servative). Sketch a phase portrait of each system. di = y(1-x2) dt
1
Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b) find the linearization at each critical point and determine the type and stability of each critical point (c) draw a phase portrait confirming the type and stability of all critical points (1) / - (2+)(y-*) V = (4-1)y + r) (2) 1-1- (4) 2 - 1 - ry (5) x = (1-1-y) V-(3--20) Bonus computational work (use technology!) 1. Uee pplane to plot the...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
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