Between synchrony and turbulence: intricate hierarchies of coexistence patterns

Synchronization modes of triple flickering buoyant diffusion flames: Experimental identification and model interpretation

The synchronization modes of a nonlinear oscillator system consisting of three identical flickering buoyant diffusion flames in isosceles triangles were studied experimentally and theoretically. Five synchronization modes, such as the in-phase, flickering death, partially flickering death, partially in-phase, and rotation modes, were experimentally observed and identified by systematically adjusting the flame distance and fuel flow rates. Two toy models were adopted to interpret the experimentally identified dynamical modes: one is the classical Kuramoto model, and the other is a complexified Stuart-Landau model, which was proposed through the introduction of the complex coupling term. The theoretical results show that the Kuramoto model successfully interpreted the dynamical modes except for those associated with amplitude death, and the complexified Stuart-Landau model well interpreted all the dynamical modes identified in our experiment. Remarkably, the proposed complexified Stuart-Landau model breaks a new path in the investigation of globally coupled nonlinear dynamical systems with identical oscillators, especially for the study of amplitude death mode.

Chimeras in globally coupled oscillators: A review

The surprising phenomenon of chimera in an ensemble of identical oscillators is no more strange behavior of network dynamics and reality. By this time, this symmetry breaking self-organized collective dynamics has been established in many networks, a ring of non-locally coupled oscillators, globally coupled networks, a three-dimensional network, and multi-layer networks. A variety of coupling and dynamical models in addition to the phase oscillators has been used for a successful observation of chimera patterns. Experimental verification has also been done using metronomes, pendula, chemical, and opto-electronic systems. The phenomenon has also been shown to appear in small networks, and hence, it is not size-dependent. We present here a brief review of the origin of chimera patterns restricting our discussions to networks of globally coupled identical oscillators only. The history of chimeras in globally coupled oscillators is older than what has been reported in nonlocally coupled phase oscillators much later. We elaborate the story of the origin of chimeras in globally coupled oscillators in a chronological order, within our limitations, and with brief descriptions of the significant contributions, including our personal experiences. We first introduce chimeras in non-locally coupled and other network configurations, in general, and then discuss about globally coupled networks in more detail.

Solitary routes to chimera states

We show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators.

Minimal nonlinear dynamical system for the interaction between vorticity waves and shear flows

This study is a direct follow-up of the paper by Heifetz and Guha [Phys. Rev. E 100, 043105 (2019)2470-004510.1103/PhysRevE.100.043105] on a minimal nonlinear dynamical system, describing a prototype of linearized two-dimensional shear instability. In that paper, the authors describe the instability in terms of an action at a distance between two vorticity waves, each of which propagates counter to its local mean flow as well as counter to the other. Here we add to the model the effect of mutual interaction between the waves and the mean flow, where growth of the waves reduces the mean shear and vice versa. This addition yields oscillatory Hamiltonian dynamics, including states of phase slipping and libration with finite-size wave amplitude oscillations. We find that wave-mean-flow dynamics emerging from unstable normal modes in the linearized stage are doomed to librate around the antiphased neutral configuration in which the waves hinder each other's counterpropagation rate. We discuss as well how the given dynamics relates to familiar models of phase oscillators.