Partial synchronization in complex networks: Chimera state, remote synchronization, and cluster synchronization

Abstract

In recent years, the study of partial synchronization of coupled oscillators in complex networks has attracted great attention. The underlying reason is both the extensive existence of the patterns of partial synchronization in brain network and their close relationship to brain functions of cognition and memory. In this paper, we briefly review the research progress in this field. According to the researches by different groups, we classify them as three types, i.e. chimera state, remote synchronization, and clustering synchronization. We mainly discuss the conditions of these three states, as well as their models, detections, and their applications in biology. We discuss the relationship among the three types of states and give some outlooks for future studies.

Gravitational Agglomeration of Local Synchronization Data Set in Innovation Ecosystem: A Game between Innovation and Institutional Governance

“…In accordance with coupled wave theory, out of sync is the norm in the innovation ecosystem [58]. If there is coupling fluctuation, there is a synchronous state in a local area [59].…”

Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure-dynamics relationship in human brain

“…To understand the underlying mechanism of these three features or how the local topologies of nodes influence their behaviors, we recall the recent findings of cluster synchronization that the oscillators of network will be automatically evolved into different synchronized clusters but the oscillators in different clusters are not synchronized with each other [ 29 , 30 ]. It was revealed that network symmetry is the necessary condition for synchronized clusters [ 31 , 32 ].…”

Effects of asymmetric coupling and boundary on the dynamic behaviors of a random nearest neighbor coupled system

“…The asymmetry of complex systems has a crucial impact on their collective behaviors. [22] Asymmetry can arise not only through the system's special network topology, but also through asymmetric coupling. In practical applications, asymmetric coupling widely exist in complex systems such as signal transmission, [23] brain neural networks, [24] swarm intelligence networks, [25] and biomolecular motors, [26] and produce rich group effects, such as stochastic resonance (SR), cluster synchronization, etc.…”