Clustered Chimera States in Delay-Coupled Oscillator Systems

Abstract

We investigate chimera states in a ring of identical phase oscillators coupled in a time-delayed and spatially nonlocal fashion. We find novel clustered chimera states that have spatially distributed phase coherence separated by incoherence with adjacent coherent regions in antiphase. The existence of such time-delay induced phase clustering is further supported through solutions of a generalized functional self-consistency equation of the mean field. Our results highlight an additional mechanism for cluster formation that may find wider practical applications.

Solvable Model for Chimera States of Coupled Oscillators

“…[2]. When brain waves are recorded, the awake side of the brain shows desynchronized electrical activity, corresponding to millions of neurons oscillating out of phase, whereas the sleeping side is highly synchronized.From a physicist's perspective, unihemispheric sleep suggests the following (admittedly, extremely idealized) problem: What's the simplest system of two oscillator populations, loosely analogous to the two hemispheres, such that one synchronizes while the other does not?Our work in this direction was motivated by a series of recent findings in nonlinear dynamics [3,4,5,6,7,8]. In 2002, Kuramoto and Battogtokh reported that arrays of nonlocally coupled oscillators could spontaneously split into synchronized and desynchronized subpopulations [3].…”

“…In two dimensions, it appeared as a strange new kind of spiral wave [5], with phase-locked oscillators in its arms coexisting with phaserandomized oscillators in its core-a circumstance made possible only by the nonlocality of the coupling. These phenomena were unprecedented in studies of pattern formation [9] and synchronization [10] in physics, chemistry, and biology, and remain poorly understood.Previous mathematical studies of chimera states have assumed that they are statistically stationary [3,4,5,6,7]. What has been lacking is an analysis of their dynamics, stability, and bifurcations.…”

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

“…Impact of coupling range R Chimera states with multiple domains of incoherence and coherence have been reported in several works and are referred to as clustered chimera or multichimera states. It is known that they may be achieved through time delay [62] or by manipulating the range of the coupling between oscillators [15][16][17]63]. The range R of the coupling reflects the migration range of the different species in the system.…”

Role of delay in the mechanism of cluster formation

“…Furthermore, communication delay naturally arises in extended systems [7]. A delay gives rise to many new phenomena in dynamical systems such as oscillation death, stabilizing periodic orbits, enhancement or suppression of synchronization, chimera state, etc [8][9][10][11][12][13][14].In this paper, we study the impact of delay on the phenomenon of phase synchronized clusters in coupled map networks. We investigate the formation of clusters on various networks namely, 1-d lattice, small-world, random, scale-free and bipartite networks [15], and provide a Lyapunov function analysis for bipartite networks to explain possible reasons behind the role of a delay on synchronized clusters.…”

“…Furthermore, communication delay naturally arises in extended systems [7]. A delay gives rise to many new phenomena in dynamical systems such as oscillation death, stabilizing periodic orbits, enhancement or suppression of synchronization, chimera state, etc [8][9][10][11][12][13][14].…”