Classify the fixed points of the following linear system and state whether they are

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  • #1
coverband
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Homework Statement



Classify the fixed points of the following linear system and state whether they are stable or unstable

[tex]\dot{x}=x + y [/tex]
[tex]\dot{y} = x + 3y [/tex]

Homework Equations



The Attempt at a Solution


Fixed point at dy/dx = 0/0. Therefore fixed point = (0,0)

How does one test for stability?

Thanks
 

Answers and Replies

  • #2
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Homework Statement



Classify the fixed points of the following linear system and state whether they are stable or unstable

[tex]\dot{x}=x + y [/tex]
[tex]\dot{y} = x + 3y [/tex]

Homework Equations



The Attempt at a Solution


Fixed point at dy/dx = 0/0. Therefore fixed point = (0,0)

How does one test for stability?

Thanks
0/0 is not a number, so how can you say that there is a fixed point at dy/dx = 0/0?
 
  • #3
coverband
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How does one test for stability?
 
  • #4
LCKurtz
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How does one test for stability?

Doesn't your text have a test for stability which involves looking at the eigenvalues of the coefficient matrix on the right side?
 

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