Can I make a force field in the xy plane that is defined with differential equations as:
x' = f_1(x,y) (speed in the x-direction is dependent on x,y coordinates)
y' = f_2(x,y) (speed in the y-direction is dependent on x,y coordinates)
So for example we can see a rigid body (such as wind) or liquid flow (such as a whirlpool) as a result of the force field.
Example is a phasediagram:
That is described with the following differential equations:
x' = x(2-x-y)
y' = y(-1+x)