Question: Differential Equation, every solution verifies

For the equation x'(t)=F(z), z=(x,y), with the vector field

F(x,y)= [- x(x^4 + y^4) - y,  x  - y(x^4+y^4)]

prove that the origin is an attractor in the future, i.e., every solution verifies:

limit as t goes to +infinity of z(t) = 0


I need to format my answer as a regular mathematical proof.



Any ideas?

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