A New Feature in Some Quasi-discontinuous Systems

Many systems can display a very short, rapid changing stage (quasi-discontinuous region) inside a relatively very long and slowly changing process. A quantitative definition for the "quasi-discontinuity" in these systems has been introduced. We have shown by a simplified model that extra-large Feigenbaum constants can be found inside some period-doubling cascades due to the quasi-discontinuity. As an example, this phenomenon has also been observed in Rose-Hindmash model describing neuron activities.