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

Example of parametric equations and parametric curves, Draw the parametric ...

Draw the parametric curve for the subsequent set of parametric equations. X = t 2 +t Y=2t-1 -1 t 1 Solution Note that the only dissimilarity here is the exis

Statistics quiz.., can someone help me with a statistics quiz?

can someone help me with a statistics quiz?

Define points, Define Points, Lines, and Spaces Points, lines, and planes...

Define Points, Lines, and Spaces Points, lines, and planes are known as undefined or primitive terms. These are the most significant and fundamental concepts in the study of geom

Help with individual questions, Hi, I''m looking for assistance/solutions t...

Hi, I''m looking for assistance/solutions to individual questions. I''ve already answered them but seek confirmation my answers are correct. I don''t want answers to a complete e

Explain different base numbers, Explain Different Base Numbers? In mult...

Explain Different Base Numbers? In multiplying or dividing two exponential expressions with different base numbers, write out the exponential expressions as products. Since

Prove that abc=60 degree, ABC is a right triangle right-angled at C and AC=...

ABC is a right triangle right-angled at C and AC=√3 BC. Prove that ∠ABC=60 o . Ans:    Tan B = AC/BC Tan B = √3 BC/BC Tan B =√3 ⇒ Tan B = Tan 60 ⇒ B = 60

the demand forecast, The King Company is producing two types of products: ...

The King Company is producing two types of products: A and B. Both products are produced on the similar machining operation. The machines operate on two 8-hour shifts, 5 days per w

Compositions of relations, Let Consider R A Χ B, S B Χ C be two relation...

Let Consider R A Χ B, S B Χ C be two relations. Then compositions of the relations S and R given by SoR A Χ C and is explained by (a, c) €(S o R) iff € b € B like (a, b) € R,

Product rule (f g)' = f ' g + f g', Product Rule: (f g)′ = f ′ g + f g′ ...

Product Rule: (f g)′ = f ′ g + f g′ As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved

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