Banded Chaos and Time-Semicrystalline Order

Abstract

Recent work has introduced the notion of a time semicrystal, a driven nonequilibrium regime in which subharmonic temporal order survives inside deterministic chaos. Here we revisit this phenomenology from the viewpoint of classical nonlinear dynamics. Banded chaotic attractors consist of a finite number of chaotic sectors cyclically permuted by stroboscopic evolution, allowing discrete subharmonic spectral components to coexist with a broadband chaotic continuum. Exemplified through the driven Duffing oscillator and the logistic map, this structure naturally reproduces the characteristic signatures of time-semicrystalline dynamics. Within this framework, periodic subharmonic motion can enter chaos through the familiar period-doubling cascade while retaining a well-defined temporal skeleton governed by the universal Feigenbaum scaling. Temporal order within chaos can also reorganize or collapse through distinct mechanisms, producing continuous or abrupt transitions that may be intertwined with symmetry changes. These results connect time-semicrystal phenomenology with established structures of dissipative nonlinear dynamics, showing that its essential ingredients already arise in standard nonlinear systems and providing a simple framework for extending and testing the paradigm in more complex, many-body, and experimental settings.