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i need show that at the following system the zero solution is nominally stable, using some change of variable that transforme in a linear system

[tex] \frac{dx}{dt}=-x + \beta (x^2+ y^2) [/tex]

[tex] \frac{dy}{dt}=-2y + \gamma x y [/tex]

i tried with the eigenvalues of the Jacobian matrix at (0,0), but one of them is positive , then the system is unstable...

[tex] \frac{dx}{dt}=-x + \beta (x^2+ y^2) [/tex]

[tex] \frac{dy}{dt}=-2y + \gamma x y [/tex]

i tried with the eigenvalues of the Jacobian matrix at (0,0), but one of them is positive , then the system is unstable...

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