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Non-linear system of ODEs

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New member
Jun 12, 2013
I need help with the following so please help me --

Consider the following non-linear system
X’ = x² - ay
Y’ = y² - y

(a) Find the fixed points of this system. (depending on a, there may be different fixed points!)

(b) Study stability of each fixed point via linearization. In the case the linearization is inconclusive, use directions of vector field analysis (or any other information contained in the equations) to show stability/instability.

(c) Use the information above to determine the bifurcation values for a, and draw the phase portraits for the system before, at, and after each bifurcation. On phase portraits identify the fixed points as well as their stable/unstable manifolds (curves) where appropriate.


Staff member
Feb 24, 2012
I have reason to believe this is part of a graded assignment. Please contact me with your professor's contact information so that I can verify that it is okay for you to receive outside help with this question.

Best Regards,

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