Symmetry breaking by power-law coupling

In-phase and anti-phase bursting dynamics and synchronisation scenario in neural network by varying coupling phase

“…Cluster formations are considered to be the intermediate stage before attaining complete synchrony [32]. Chimeras can be induced in a network by distance dependent coupling [33,34], non local coupling [35], cross coupling or rotation matrix coupling [23], modifications in initial conditions and topology [36] or just as an inherent property where the incoherent sub population stabilises the coherent sub population [37]. Whatever may be the mechanism behind chimera state, the underlying principle is symmetry breaking [38].…”

Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging

“…Complex systems abound in nature, both in the forms of man-made systems and natural systems, including power grid, internet, social network, neural network, and so on. Depending on the network geometries, system parameters, and interaction among the dynamical ensembles, such complex systems exhibit various collective behaviors, including synchronization [1,2,3], clustering [4,5], solitary state [6,7,8,9], chimera [10,11,12,13,14,15,16], and oscillation quenching [17,18,19,20,21,22,23]. Each of these dynamical states implies a great significance with the many real-world instances.…”