Graphical representation of a dynamical system

If we consider the dynamical system:
    x=y;
    y=y*y+x+y;
  
in the window of values of x,y from -4 to 4,it is represented here as an attractor starting from three different points:

This is the limit set representation and is different for each starting point in the chosen window. Instead the escape time representation:

is unique in the chosen window.

Finally here is the "global" representation which is also unique in the window: