Model of globally coupled Duffing flows

A Duffing oscillator in a certain parameter range shows period-doubling that has the same Feigenbaum ratio as the logistic map, which is an important issue in universality in chaos. In this paper a globally coupled lattice of Duffing flows (GCFL), which is a natural extension of the globally coupled logistic map lattice (GCML), is constructed. It is observed that GCFL inherits various intriguing properties of GCML and that universality at the level of elements is thus lifted to that of systems. Phase diagrams for GCFL are determined, which are essentially the same as those for GCML. Similar to the two-clustered periodic attractor of GCML, the GCFL two-clustered attractor exhibits a successive period-doubling with an increase of population imbalance between the clusters ( $\vartheta $ -bifurcation). A nontrivial distinction between the GCML and GCFL attractors that originates from the symmetry in the Duffing equation is investigated in detail