Spiral Wave Chimeras in Complex Oscillatory and Chaotic Systems

Abstract

We demonstrate for the first time that spiral wave chimeras-spiral waves with spatially extended unsynchronzied cores-can exist in complex oscillatory and even locally chaotic homogeneous systems under nonlocal coupling. Using ideas from phase synchronization, we show in particular that the unsynchronized cores exhibit a distribution of different frequencies, thus generalizing the main concept of chimera states beyond simple oscillatory systems. In contrast to simple oscillatory systems, we find that spiral wave chimeras in complex oscillatory and locally chaotic systems are characterized by the presence of synchronization defect lines (SDLs), along which the dynamics follows a periodic behavior different from that of the bulk. Whereas this is similar to the case of local coupling, the type of the prevailing SDLs is very different.

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

“…Since their first discovery a decade ago many theoretical investigations of coupled phase oscillators and other simplified models have been carried out [6,7], but their experimental observation in real systems was only reported very recently in optical light modulators [8], optical comb [9], chemical [10], mechanical [11,12], electronic [13], and electrochemical [14,15] oscillator systems. Theoretical studies have found chimeras also in other systems, including higher-dimensional systems [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].…”

“…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].…”

Chimeras in networks with purely local coupling

“…Spatial networks on which they have been studied include a one-dimensional ring [2,[4][5][6][7][8], a square domain without periodic boundary conditions [9][10][11], a torus [12,13] and a sphere [14]. They have also been observed recently in a number of experimental settings [15][16][17][18][19].…”

Взаимодействие Химерных Состояний В Многослойной Сети Нелокально Связанных Осцилляторов

“…В данном контексте было рассмотрено образование химерных состояний как в одномерных си-стемах (цепочках связанных осцилляторов) [3], так и в распределенных системах, состоящих из эквидистантно расположенных осцилляторов, описывающихся уравнениями Ресслера [4], Фитцхью-Нагумо [5] и др. Химерные состояния были обнаружены в сетях с различной топологией связей.…”