If the eigenvalues from a linearized system of non-linear differential equations indicate a fixed point at the origin is an unstable spiral, yet the non-linearized system shows that a limit cycle exists at the circle r=1, do we still classify the origin as an unstable spiral even though it approaches the limit cycle?   In other words, does an unstable spiral have to approach infinity as time increases?  Or can we say an unstable spiral approaches a limit cycle? I'm wondering how do we classify the stability of the origin when a limit cycle exists?  Hope this makes sense.

Q: At any given time, a subatomic particle can be in one of two states, and it moves randomly from one…

A: A particle be in one of two states and it move one state to another state.

Q: Define Sturm-Liouville Eigenvalue Problem in Standard Form?

A:

Q: Q2) find eigenvalue eigenvector of A x(0,0) = (1,1)

A: Eigenvalues and Eigenvectors of the matrix

Q: 10. Prove that the eigenvalue problem y" + dy = 0; y(0) = 0, y(1) + y'(1) = 0 %3D has no negative…

A:

Q: Apply the eigenvalue method of this section to find a general solution of the given system. If…

A: According to the given information it is required to determine the solution of given system by…

Q: Consider the eigenvalue problem y" + 2y' + ày = 0; y(0) = y(1) = 0. Show that there is no eigenvalue…

A:

Q: 2. Show that eigenvalues A of the boundary value problem y" + (Ar +a)y = 0, y(0) – /(1) = 0, y/(0) +…

A: Given:   y"+(λx+x2)y=0, y(0)-y'(1)=0, y(0)+y'(1)=0

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  A must have two…

A:

Q: Suppose that for a diatomic molecule the Hamiltonian has the form Ĥ : В 2а a)Calculate the…

A: Given: The diatomic molecule includes the Hamiltonian matrix as follows,

Q: Determine the eigenvalue of the following system in terms of a then find the critical values at…

A: Given: The system     x' = α1-1αx Consider the coefficient matrix     A=α1-1α To determine the…

Q: Suppose that a patient receives a daily dose of 50mg/L of a certain drug such that 42% of it is…

A: Suppose that xt denotes the concentration of drug in mg/L , t days after the monday. Given that : x0…

Q: To every eigenvaluebof a sturm liouville system there corresponds only one linearly independent…

A:

Q: Consider the eigenvalue problem X" (x) -pX(x) = 0 (0 < x < 1) X'(0) = -X(0), X'(1) = -X(1), where p…

A: Given  X''(x)-pX(x)=0  , 0&lt;x&lt;1 …………………1 Boundary condition: X'(0)=-12X(0) , X'(1)=-X(1)

Q: 3. If the eigenvalues of A are 2 and -1, with multiplicities 2 and 3, respectively, find the…

A: One of the  Eigen values is 2 with multiplicity 2 The second  Eigen value -1 is with multiplicity 3…

Q: Example 1. Prove that the homogeneous integral equation o(x) =À (3x - 2) to(t) dt %3D has no…

A: Solution

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  A must have atleast…

A:

Q: Use the method of separation of variables to construct the energy eigenfunctions for the particle…

A: Given equation: -h22m∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2=EnΦn(x,y), ∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2=-2mh2EnΦn(x,y),…

Q: The following is a phase portrait for a system of nonlinear differential equations. Give the…

A: We are given the phase potrait of a nonlinear dynamic system, and we have to find the posible…

Q: (a) Consider the eigenvalue problem - X" = AX, X'(0) + X(0) = 0, X(I) = 0. 0 < x < /

A:

Q: 15. If the point of stability is stable but not asymptotically then the eigenvalues are

A:

Q: d the three distinct real eigenvalues of the matrx B=-3 1 -2 6.

A:

Q: Give brief Explanation of Special Case of a Repeated Zero Eigenvalue?

A: In this question, we have to give the brief explanation of special case of repeated zero Eigen…

Q: A E M, has only real eigenvalues, show that A is similar to A

A:

Q: How can I show that a twice continuously differentiable function with a lipschitz continuous hessian…

A: Let f be the twice continuously differentiable function with a lipschitz continuous hessian with all…

Q: = Show that the following SL problem has a negative eigenvalue y"(x) + Ay(x) = 0, y'(0) = 0, (y(1) –…

A:

Q: What do you mean by Real Eigenvalues?

A:

Q: We can find another solution to a system of differential equations with repeated eigenvalues by…

A: Statement is false. we use variation of parameters to find a particular solution of  non homogeneous…

Q: Find the Eigenvalues and Eigenfunctions of the following Sturm_Liouville problems posed. y´´ +2y´ +…

A: Given the equation: ay(x)+2ddxy(x)+d2dx2y(x)=0This differential equation has the form: y'' + p*y' +…

Q: What does the smallest eigenvalue do in a real-life application?

A: The eigen values are used on a daily basis sub-consciously most of the time. However it have various…

Q: 1 1 1 1

A:

Q: A is a 3 X 3matrix with eigenvectors v1 ,v2 and v3 corresponding to eigenvalues λ1 = -1/3,λ2=1/3 and…

A:

Q: For part (a), a 1-eigenvector of A for would also be correct) For part (h

A:

Q: Let vn = be the solution to the discrete dynamical system: Yn 6xn – 13yn Yn+1 = 0xn – 7yn Xn+1 -3 If…

A: Using diagonalisation of the coefficients matrix.

Q: Consider the eigenvalue problem           y"+2y'+(lambda)y=0;     y(0)=0,       y'(1)=0. Show that…

A:

Q: 3y1 + 2y2 -6y1 – 5y2 Ул (0) — 0 Y2 (0) = 4

A:

Q: Find the smallest (in absolute value) eigenvalue using

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If A 3 = A, what are the possible eigenvalues of A?

A:

Q: Write the homogeneous part of the differential equation system, namely f (x) = g(x) = 0 obtained…

A:

Q: 27.If both eigenvalues are negative the critical point

A: If both eigen values are negative, the critical point is a stable node; the trajectories are…

Q: find eigenvectors, and solve. Classified the type of equilibrium point at the origin, and sketch the…

A: We are given a system of linear homogeneous differential equations and we have to solve it using…

Q: [15] Solve the eigenvalue problem X"(x) + X'(x) - XX(x) = 0 X (0) = 0, X(a) = 0. 0<x<a,

A: Given : The equation is  X''(x)+X'(x)-λX(x)=0   where 0&lt;x&lt;aX(0)=0 and X(a)=0 To find : The…

Q: If A3=A,what are the possible eigenvalues ofA .

A: If A3=A, what are the possible eigenvalues of A.

Q: 1. Find the eigenvalues of A and the corresponding eigenvectors. 2. Use the results in 1. above to…

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: In ethod of eigenfunction expansions he methC 15. y(0) 0, y(1)-0

A: Given differential equation is y" = -x , y(0)=0 &amp; y(1)=0

Q: Suppose a system of first-order linear differential equations has eigenvalues A₁-3, A2=-2.3. The…

A: Let a system of first order differential equation has two eigen values λ1 and λ2, then the origin is…

Q: What do you mean by Defective Eigenvalues?

A: Defective Eigenvalues: If the algebraic multiplicity of λ exceeds its geometric multiplicity, then λ…