Model of Globally Coupled Duffing Flows

TL;DR

This paper introduces a globally coupled lattice of Duffing flows, extending the logistic map lattice, and demonstrates that universality in chaos phenomena is preserved at the system level, with detailed phase diagrams and attractor behaviors analyzed.

Contribution

It constructs a new model of globally coupled Duffing flows and shows that properties of logistic map lattices are extended to this continuous-time system, revealing universality in chaos.

Findings

GCFL inherits properties of GCML

Phase diagrams are similar between GCFL and GCML

Two-clustered attractors exhibit period-doubling

Abstract

A Duffing oscillator in a certain parameter range shows period-doubling that shares the same Feigenbaum ratio with the logistic map, which is an important issue in the 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 of GCFL are determined, which are essentially the same with those of 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. A non-trivial distinction between the GCML and GCFL attractors that originates from the symmetry in the Duffing equation is investigated in detail.