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Stablity of a 2D recursive relation near a fixed point

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Observe that (0,0) is a fixed point of the system:

x_(n+1) = u*x_n - y_n + (y_n)^2
y_(n+1) = x_n + (x_n)^4 + y_n

Regardless of the choice of parameter u. Determine the range of u values for which this fixed point is stable.

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Solution:

To investigate stability near a fixed point, we linearize the equation near the ...

Solution Summary

The stability of a 2D recursive relation near a fixed point is examined. The range of u values for which this fixed point is stable is examined.

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