The effect of an applied rf signal on the radiation emitted from a long Josephson junction is examined by means of a model based on the sine-Gordon equation. This system exhibits a variety of interesting phenomena, e.g., chaos and hysteresis. The hysteresis loop is examined in detail. These simple analyses show that for rf frequencies larger than a certain threshold value no hysteresis is expected. This is verified in numerical simulations where the frequency and length of the junction have been varied.