Characteristics of period-doubling bifurcation cascades in quasi-discontinuous systems

Many systems can display a very short, rapid change stage (quasi-discontinu ous region) inside a relatively very long and slow change process. A quanti tative definition for the "quasi-discontinuity" in these systems has been i ntroduced. With the aid of a simplified model, some extraordinary Feigenbau m constants have been found inside the period-doubling cascades, the relati onship between the values of the extraordinary Feigenbaum constants and the quasi-discontinuity of the system has also been reported. The phenomenon h as been observed in Pikovsky circuit and Rose-Hindmash model.