Question

Consider the following nonlinear system: x'(t) = x - y, y'(t) = (x^2-4)y a. Determine the...

Consider the following nonlinear system: x'(t) = x - y, y'(t) = (x^2-4)y

a. Determine the equilibria.

b. Classify the equilibria using linearization.

c. Use the nullclines to draw the phase portrait.

Please write neatly. Thanks!

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
following nonlinear system: x' = 2 sin y, y'= x^2 + 2y − 1 find all...
following nonlinear system: x' = 2 sin y, y'= x^2 + 2y − 1 find all singular points in the domain x, y ∈ [−1, 1],determine their types and stability. Find slopes of saddle separatrices. Use this to sketch the phase portrait in the domain x, y ∈ [−1, 1].
Given a nonlinear system   x(t)" + cx(t)' + sin(x(t)) = 0                       (3-1) a) Consider its phase...
Given a nonlinear system   x(t)" + cx(t)' + sin(x(t)) = 0                       (3-1) a) Consider its phase plane by assuming proper parameters of c. Do you have singular points with the cases of CENTER FOCUS, NODE and SADDLE ? Are those stable? asymptotic stable or unstable? b) When c = 0, plot the phase plane and find these singular points
Consider the function f(x,y)= (x+2*y)*e^(x-2y) for all real values (x,y). Determine the linearization to f at...
Consider the function f(x,y)= (x+2*y)*e^(x-2y) for all real values (x,y). Determine the linearization to f at the point (2,1) Use the linearization to approximate f(2.1,1.1)
Consider the linear first order system [16] x′ = x + y (1) y′ =4x−2y. (2)...
Consider the linear first order system [16] x′ = x + y (1) y′ =4x−2y. (2) (a) Determine the equilibria of System (1)-(2) as well as their stability. [6] (b) Compute the general solution of System (1)-(2). [6] (c) Determine the solution of the initial value problem associated with System (1)-(2), with initial condition x(0) = 1, y(0) = 2.
Consider a system defined by the input-output relationship given below: y(t) = x(t)x(t-2) a) Is the...
Consider a system defined by the input-output relationship given below: y(t) = x(t)x(t-2) a) Is the system memoryless? Why? b) Is the system stable? Why? c) Is the system causal? Why? d) Is the system invertible? Show why? e) Find the impulse response of the system. PLEASE ANSWER ALL QUESTIONS!
Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = −y −...
Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = −y − x(x2 + y2)2 y' = x − y(x2 + y2)2,   X(0) = (3, 0) (r(t), θ(t)) =
Consider the following difference equation for populations called the nonlinear logistic model ?t+1=?xt(1−xt) (a) Find the...
Consider the following difference equation for populations called the nonlinear logistic model ?t+1=?xt(1−xt) (a) Find the equilibria. Here ?>0 is an unknown parameter (i.e., is a constant). (b) Determine the values of r for which each equilibrium is stable.
Assignment #3 Modeling and the Geometry of Systems 1. For this problem, we study the nonlinear...
Assignment #3 Modeling and the Geometry of Systems 1. For this problem, we study the nonlinear differential equation: dx dt = y dy dt = x − x^3 − y^3 a) Algebraically determine all of the equilibria to the differential equation . b) For a solution {x(t), y(t)} with {x(0), y(0)} = {x0, y0}, use your phase diagram to describe the long term behavior of the solution. 1. {x0, y0} = {1, 1} 2. {x0, y0} = {−1, −1} 3....
Consider the transformation T: R2 -> R3 defined by T(x,y) = (x-y,x+y,x+2y) Answer the Following a)Find...
Consider the transformation T: R2 -> R3 defined by T(x,y) = (x-y,x+y,x+2y) Answer the Following a)Find the Standard Matrix A for the linear transformation b)Find T([1 -2]) c) determine if c = [0 is in the range of the transformation T 2 3] Please explain as much as possible this is a test question that I got no points on. Now studying for the final and trying to understand past test questions.
Consider the differential equation x′=[2 −2 4 −2], with x(0)=[1 1] Solve the differential equation wherex=[x(t)y(t)]...
Consider the differential equation x′=[2 −2 4 −2], with x(0)=[1 1] Solve the differential equation wherex=[x(t)y(t)] please write as neat as possible better if typed and explain clearly with step by step work
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT