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.