Experimental observation of chimera and cluster states in a minimal globally coupled network

Abstract

A "chimera state" is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic optoelectronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.We provide experimental evidence of chimera and cluster synchronous states in a globally coupled network of four opto-electronic oscillators. Since this is the minimal network in which a chimera state can occur, our apparatus provides the ability to experimentally test some of the fundamental properties of chimera states. Cluster synchronization has thus far been studied independently of chimera states; however, here we present a unified approach that exploits the symmetries in the network to determine the stability of chimeras and clusters. We obtain two important results: A) we provide a first experimental demonstration that chimeras can appear in small networks, contrary to the conventional assumption that a large network with non-local coupling is necessary 1 , and B) we show that both cluster states and chimera states can be regarded as special cases of the more general phenomenon of partial synchronization. The methods apply to networks of different size and topology, opening up potential applications to chimeras and other partial synchrony patterns in real world networks such as power grids.

Smallest chimera states

“…First, it has been observed that these states can exist in small networks of as few as 4 phase oscillators [27][28][29][30] and also in the model of semiconductor lasers [31]. Experimentally, chimera states of this type have been recently observed in small networks of optoelectronic oscillators [32] as well as coupled pendula [33,34].In the Letter, we show that the weak chimera patterns which are characterized by two frequency synchronized oscillators and one evolving with different frequency can be observed in the networks of 3 identical nodes. As the proof of the concept we use a network of Kuramoto oscillators with inertia.…”

“…First, it has been observed that these states can exist in small networks of as few as 4 phase oscillators [27][28][29][30] and also in the model of semiconductor lasers [31]. Experimentally, chimera states of this type have been recently observed in small networks of optoelectronic oscillators [32] as well as coupled pendula [33,34].…”

Коллективная Динамика Идентичных Бистабильных Автогенераторов С Запаздыванием, Связанных Через Общее Поле

“…Отметим, что шести генераторов оказывается достаточно для возник-новения состояния " химера". Как было недавно показано в работе [13], состояния " химера" могут существовать в ансамблях, состоящих всего лишь из четырех идентичных осцилляторов.…”

“…Состояния " химера" были сначала обнаружены в ансамблях фазовых осцилляторов, связь между которыми является локальной [6], нелокаль-ной [5] или глобальной [7], а затем и в ансамблях, элементы которых не являются фазовыми осцилляторами [8][9][10]. Состояния " химера" были обнаружены не только при теоретических, но и при экспериментальных исследованиях [11][12][13].…”

Collective dynamics of identical bistable self-sustained oscillators with delayed feedback coupled via a mean field

“…Chimera states were first discovered in ensembles of phase oscillators with local [6], nonlocal [5], or global coupling [7] and then also found in ensembles with elements not representing phase oscillators [8][9][10]. Chimeras were not only theoretically predicted, but also observed in experimental investigations [11][12][13].…”