We present examples of simple dynamical systems containing alternative routes to chaos which are degenerate with a period-doubling route. The existence of degenerate routes implies the possibility of having more entangled dynamical behaviors hidden in observations based on a single-variable time series, possibly requiring, therefore, special care to discriminate them. A model system allowing th...

In this paper, the dynamics of multicellular chopper are considered. The model is described by a continuous time three--dimensional autonomous system. Some basic dynamical properties such as Poincar'e mapping, power spectrum and chaotic behaviors are studied. Analysis results show that this system has complex dynamics with some interesting characteristics.

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these situations the dynamical behavior is exactly describable through infinite families of Tsallis’ q-expon...

Cascades of period-doubling bifurcations have attracted much interest from researchers of dynamical systems in the past two decades as it is one of the routes to onset of chaos. In this paper we consider routes to onset of chaos involving homoclinic-doubling bifurcations. ∗Partially supported by Grant-in-Aid for Scientific Research (No. 08740139), Ministry of Education, Science and Culture, Japan.