Stability and chaos are analyzed by computing the Lyaponuv exponent which is plotted above.

A plot of z = |W(x+iy)|, where W is the Lambert W function

A plot of the complex valued function (z-2)²(z+1-2i)(z+2+2i)/z³ by Hans Lundmark

Plot of the equation Sin(xSin(y)) = Cos(yCos(x)) by Xah Lee

http://demonstrations.wolfram.com/CosineOffsetCurves/