Amplitude-phase coupling drives chimera states in globally coupled laser networks

Abstract

For a globally coupled network of semiconductor lasers with delayed optical feedback, we demonstrate the existence of chimera states. The domains of coherence and incoherence that are typical for chimera states are found to exist for the amplitude, phase, and inversion of the coupled lasers. These chimera states defy several of the previously established existence criteria. While chimera states in phase oscillators generally demand nonlocal coupling, large system sizes, and specially prepared initial conditions, we find chimera states that are stable for global coupling in a network of only four coupled lasers for random initial conditions. The existence is linked to a regime of multistability between the synchronous steady state and asynchronous periodic solutions. We show that amplitude-phase coupling, a concept common in different fields, is necessary for the formation of the chimera states. Synchronization is a common phenomenon in interacting nonlinear dynamical systems in various fields of research such as physics, chemistry, biology, engineering, or socioeconomic sciences [1][2][3]. While a lot of knowledge has been gained on the origin of complete synchronization, more complex partial synchronization patterns have only recently become the focus of intense research. We still lack a full understanding of these phenomena, and a very prominent example are chimera states where an ensemble of identical elements self-organizes into spatially separated coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics [4,5]. Since their first discovery a decade ago many theoretical investigations of coupled phase oscillators and other simplified models have been carried out [6,7] [7,16,17], e.g., spiral wave chimeras [18,19], FitzHugh-Nagumo neural systems [20], Stuart-Landau oscillators [21][22][23], where pure amplitude chimeras [24] were found, or quantum interference devices [25]. In real-world systems chimera states might play a role, e.g., in the unihemispheric sleep of birds and dolphins [26], in neuronal bump states [27,28], in power grids [29], or in social systems [30].Although no universal mechanism for the formation of chimera states has yet been established, three general essential requirements have been found in many studies: (i) a large number of coupled elements, (ii) non-local coupling, and (iii) specific initial conditions. These were primarily derived from the phase oscillator model [7] but also apply to other systems. If these conditions are not met, the chimera states tend to have very short lifetimes. Recent studies, however, suggest that these paradigms can be broken and chimera states are observed also for small system sizes [31], global coupling [15,23,32,33] and random initial conditions [34].Surprisingly, chimera states appear at the interface of independent fields of research putting together different scientific communities. Recent examples are quantum chimera state [35] or coexistence of coherent and incoherent patterns with respect to the modes of an optical com...

Multiplexed networks: reservoir computing with virtual and real nodes

“…The sign of the real part of the nonlinearity  g Î defines whether the Andronov-Hopf-bifurcation is sub-or supercritical, while the imaginary part defines the hardness of the spring and induces an amplitude-phase coupling. Hence, Im(γ) is linked to the amplitudephase or linewidth-enhancement factor of semiconductor lasers [35]. The network-coupling between the oscillators is defined by the coupling strength  k Î and coupling phase f p Î [ ] 0, 2 .…”

Mechanisms of appearance of amplitude and phase chimera states in ensembles of nonlocally coupled chaotic systems

“…The chimera states were firstly described in a system of coupled phase oscillators [2]. Since then, they were also found in a wide range of different models including both discrete-time maps and continuous-time (differential) systems with regular and chaotic dynamics [8,9,10,11,12,13,14,15]. The existence of chimera states was repeatedly confirmed not only numerically but also experimentally [16,17,18,19].…”

Nonlinear and Nonequilibrium Dynamics of Quantum-Dot Optoelectronic Devices

“…Furthermore, their complex dynamics allow for the studying of many generic nonlinear phenomena in a comparably simple experimental setup [LAR10]. For example, the appearance of chimera states -coexisting coherent and incoherent states in coupled dynamic systems -has been recently predicted in coupled laser networks, with the amplitude-phase coupling as a driving force [BOE15].…”