Question

Discuss the bifurcation of the given nonlinear systems. x˙=r^2 - x^2

Discuss the bifurcation of the given nonlinear systems.

x˙=r^2 - x^2

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar 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)) =
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/sqrt(x^2+y^2)](16 − x2 − y2) y'= [-x-y/sqrt(x^2+y^2)](16 − x2 − y2) X(0) = (1, 0)
3. Consider the nonlinear oscillator equation for x(t) given by ?13 ? x ̈+ε 3x ̇...
3. Consider the nonlinear oscillator equation for x(t) given by ?13 ? x ̈+ε 3x ̇ −x ̇ +x=0, x(0)=0, x ̇(0)=2a where a is a positive constant. If ε = 0 this is a simple harmonic oscillator with frequency 1. With non-zero ε this oscillator has a limit cycle, a sort of nonlinear center toward which all trajectories evolve: if you start with a small amplitude, it grows; if you start with a large amplitude, it decays. For ε...
Consider the nonlinear second-order differential equation 4x"+4x'+2(k^2)(x^2)− 1/2 =0, where k > 0 is a constant....
Consider the nonlinear second-order differential equation 4x"+4x'+2(k^2)(x^2)− 1/2 =0, where k > 0 is a constant. Answer to the following questions. (a) Show that there is no periodic solution in a simply connected region R={(x,y) ∈ R2 | x <0}. (Hint: Use the corollary to Theorem 11.5.1>> If symply connected region R either contains no critical points of plane autonomous system or contains a single saddle point, then there are no periodic solutions. ) (b) Derive a plane autonomous system...
Given f(x) = x4 – 4x3, graph the nonlinear function and answer the following: a) What...
Given f(x) = x4 – 4x3, graph the nonlinear function and answer the following: a) What coordinates are the absolute minimum? b) The function is concave downward for c) The function is increasing for what values of X? d) What are the X- intercepts? e) What coordinates are the inflection point?
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].
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!
Use Scilab to solve the following set of nonlinear algebraic equations: x^3y -4y^2 +3x = 1...
Use Scilab to solve the following set of nonlinear algebraic equations: x^3y -4y^2 +3x = 1 and 6y^2 - 9xy= 5 with initial guesses of x = 2, y = 2.
Write a MatLab code J = Jcb(X) that computes the jacobian of a nonlinear vector of...
Write a MatLab code J = Jcb(X) that computes the jacobian of a nonlinear vector of functions of X. Input X is a vector of unkown functions of X and output J is the jacobian of the nonlinear vector function of X.
The marginal revenue of a company is given by r(x)=x^3-0.3x^2+0.1 and the marginal cost is given...
The marginal revenue of a company is given by r(x)=x^3-0.3x^2+0.1 and the marginal cost is given by c(x)=x\sqrt{-x^2+100} both measured in thousands of dollars per hundred units (x) produced. Find the total profit for x=1 to x=4 hundred units produced.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT