To find whether the given diagram is for the parameter h > 0 or h < 0 . Concept Introduction: Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric. Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases. Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

Question

Want to see the full answer?

Answer 1

Question

Chapter 3.6, Problem 1E

Interpretation Introduction

Interpretation:

To find whether the given diagram is for the parameter h > 0 or h < 0.

Concept Introduction:

Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.

Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.

Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Page < 2 of 2 - ZOOM + The set of all 3 x 3 upper triangular matrices 6) Determine whether each of the following sets, together with the standard operations, is a vector space. If it is, then simply write 'Vector space'. You do not have to prove all ten vector space axioms. If it is not, then identify one of the ten vector space axioms with its number in the attached sheet that fails and also show that how it fails. a) The set of all polynomials of degree four or less. b) The set of all 2 x 2 singular matrices. c) The set {(x, y) : x ≥ 0, y is a real number}. d) C[0,1], the set of all continuous functions defined on the interval [0,1]. 7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and show that it is orthogonal to both u and v. 8) a) Find the equation of the least squares regression line for the data points below. (-2,0), (0,2), (2,2) b) Graph the points and the line that you found from a) on the same Cartesian coordinate plane.

Page < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.

Please help solve the following whilst showing all working out. Is part of exam revision questions but no solution is given