The influence of an applied rf signal on the emitted radiation from a large area Josephson junction is examined. A model of the system is presented in the framework of the one-dimensional sine-Gordon equation. The model linearizes for small and large values of the amplitude of the applied signal. In the intermediate regime lower and upper threshold values (for the amplitude) for transition to chaos are found. Feigenbaum period doubling (period-doubling bifurcation cascade) appears when chaos is approached for increasing amplitude. The findings are supported experimentally. Applied Physics Letters is copyrighted by The American Institute of Physics.