Question: leading behavior of curves


I need your help, to find all possible leading behavior of the following curves as x ->infinity of the following curves  defined using the implicit equation:

implicitplot(x^2*y^2-2*x*y^3+y^4-y^3+x^2 = 1, x = 100 .. 1000, y = 0 .. 1000);

Maybe we must change the range of y or x to conclude and obtain all possibles behavior.

I hope have any idea to conclude.

many thanks



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