System differential equations

  • Thread starter dirk_mec1
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Homework Statement



Determine the equibrilium solutions and their stability properties of the system below:


[tex]
\dot{x} = (1-z)[(4-z^2)(x^2+y^2-2x+y)-4(-2x+y)-4]
[/tex]

[tex]
\dot{y} = (1-z)[(4-z^2)(xy-x-zy)-4(-x-zy)-2z]
[/tex]

[tex]
\dot{z} = z^2(4-z^2)(x^2+y^2)
[/tex]



The Attempt at a Solution


The critical point (0,0,1) is difficult to characterise since the eigenvalues are 0, 0, 0. However you can determine stabilitity of this point by looking at the flow of z' ... but how?
 

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