The transition from solitons to chaos in the solution of the logistic equation

The discrete logistic map was one of the first equations to be studied for the production of chaos. We shall show that a soliton solution exists for the differential logistic equation when the output is the derivative of the dependent variable rather than the variable itself. Furthermore, when the logistic equation is solved using Euler's forward algorithm a transition from a soliton solution to chaos exists and can be accurately predicted. The results are used directly to design an electronic soliton generator.