Abstract
A curious dynamical behavior known as period doubling and chaos is shared by Josephson junctions and simple recursive mathematical systems. This is in spite of their very different descriptions in terms of second-order, non-linear differential equations on the one hand and first-order, non-linear difference equations on the other. I show that phase-locked loops provide a bridge between the two types of systems. It appears that the limiting behavior, as chaos is approached by increasing some system parameter (for example, the amplitude of microwave excitation of the Josephson junction), is quantitatively identical — to a high degree of precision — in many different systems.
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