Networks of coupled oscillators: From phase to amplitude chimeras

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 28, 113124 (2018) and may be found at https://doi.org/10.1063/1.5054181.We show that amplitude-mediated phase chimeras and amplitude chimeras can occur in the same network of nonlocally coupled identical oscillators. These are two different partial synchronization patterns, where spatially coherent domains coexist with incoherent domains and coherence/incoherence referring to both amplitude and phase or only the amplitude of the oscillators, respectively. By changing the coupling strength, the two types of chimera patterns can be induced. We find numerically that the amplitude chimeras are not short-living transients but can have a long lifetime. Also, we observe variants of the amplitude chimeras with quasiperiodic temporal oscillations. We provide a qualitative explanation of the observed phenomena in the light of symmetry breaking bifurcation scenarios. We believe that this study will shed light on the connection between two disparate chimera states having different symmetry-breaking properties. Chimera states are emergent dynamical patterns in networks of coupled oscillators where coherent and incoherent domains coexist due to spontaneous symmetry-breaking. In oscillators that exhibit both phase and amplitude dynamics, two types of distinct chimera patterns exist, namely, amplitude-mediated phase chimeras (AMCs) and amplitude chimeras (ACs). In the AMC state coherent and incoherent regions are distinguished by different mean phase velocities: all coherent oscillators have the same phase velocity, however, the incoherent oscillators have disparate phase velocities. In contrast to AMC, in the AC state, all the oscillators have the same phase velocity, however, the oscillators in the incoherent domain show periodic oscillations with randomly shifted center of mass. Surprisingly, in all the previous studies on chimeras, a given network of continuous-time dynamical systems seems to show either AMC or AC: they never occur in the same network. In this paper, for the first time, we identify a network of coupled oscillators where both AMC and AC are observed in the same system, and we also provide a qualitative explanation of the observation based on symmetry-breaking bifurcations.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept