SYSTEMS OF ODE, Mathematics

Assignment Help:
Problem 1 Let ~x0 = A~x and y
0 = B~y be two 2  2 linear systems of ODE.
(1) Suppose that A and B have the same purely imaginary eigenvalues. Prove that these systems
are topologically conjugate.
(2) Suppose that A and B have di erent purely imaginary eigenvalues. Prove that the ODE
systems are not topologically conjugate.
(3) Suppose A has eigenvalues 0,  and B has eigenvalues 0, . Prove theta the ODE systems are
topologically conjugate if and only if and  have the same sign.
(4) Prove that if A has purely imaginary eigenvalues, and B has real eigenvalues, then the ODE
systems are not topologically conjugate.
(5) Use the information above as well as the theorems from class to provide complete classi cation
of dynamics two-dimensional linear systems of ODE by conjugacy

Related Discussions:- SYSTEMS OF ODE

Innovation, In the innovations algorithm, show that for each n = 2, the inn...

In the innovations algorithm, show that for each n = 2, the innovation Xn - ˆXn is uncorrelated with X1, . . . , Xn-1. Conclude that Xn - ˆXn is uncorrelated with the innovations X

Reason for why limits not existing, Reason for why limits not existing : I...

Reason for why limits not existing : In the previous section we saw two limits that did not.  We saw that did not exist since the function did not settle down to a sing

Find the value of the derivative, Given y = f(x) = x 2 + 2x +3 a) Use the ...

Given y = f(x) = x 2 + 2x +3 a) Use the definitional formula given below to find the derivative of the function. b) Find the value of the derivative at x = 3.

Find out the determinant, Find out the determinant: Find out the deter...

Find out the determinant: Find out the determinant of the following 3 x 3 matrix, expanding about row 1. Solution:

Mathematical science, state tha different types of models used in operation...

state tha different types of models used in operations research.

Vectors, If r,R denote position vectors of points on the straight lines in ...

If r,R denote position vectors of points on the straight lines in the direction of a and b respectively, and if n is a unit vector perpendicular to both these directions, show that

Calculus, sin(xy)+x=5y Find the derivative.

sin(xy)+x=5y Find the derivative.

Modeling - nonhomogeneous systems, Under this section we're going to go bac...

Under this section we're going to go back and revisit the concept of modeling only now we're going to look at this in light of the fact as we now understand how to solve systems of

Pre-operational stage-development learning maths, Pre-operational Stage : ...

Pre-operational Stage :  This period of a child's cognitive development usually begins at the age of 2, and lasts until about the age of 6. Thus, it usually coincides with the pre

Relative maximum point, Relative maximum point The above graph of the ...

Relative maximum point The above graph of the function slopes upwards to the right between points C and A and thus has a positive slope among these two points. The function ha

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd