Controlling cluster synchronization by adapting the topology

Abstract

We suggest an adaptive control scheme for the control of in-phase and cluster synchronization in delay-coupled networks. Based on the speed-gradient method, our scheme adapts the topology of a network such that the target state is realized. It is robust towards different initial condition as well as changes in the coupling parameters. The emerging topology is characterized by a delicate interplay of excitatory and inhibitory links leading to the stabilization of the desired cluster state. As a crucial parameter determining this interplay we identify the delay time. Furthermore, we show how to construct networks such that they exhibit not only a given cluster state but also with a given oscillation frequency. We apply our method to coupled Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in an expansion of systems close to a Hopf bifurcation. The successful and robust control of this generic model opens up possible applications in a wide range of systems in physics, chemistry, technology, and life science.

Partial synchronization and partial amplitude death in mesoscale network motifs

“…Synchronized behavior is in some cases considered essential for the proper functioning of the network (e.g., power distribution networks [20] or coherent circadian output in mammals [21,22]) while in others it is undesired and harmful (e.g., in several pathological neuronal states such as Parkinson's disease and essential tremor [23,24]). Thus the control of synchronization has also widely been studied [25][26][27][28].…”

Horizons of cybernetical physics

“…Recent studies led also to discovery of more complex synchronization-related phenomena like cluster synchronization [121][122][123], chimaera states [124][125][126][127], polarization [128,129], motifs [130][131][132], etc. Schöll and his group have valuable contributions into development of most of those new concepts.…”

Synchronization of two Rössler systems with switching coupling

“…Although the connectivity among the dynamical units is usually considered time-invariant, interaction among dynamical systems may also occur in a discontinuous way (for instance, when it is mediated by links activated according to the relative distance of mobile units [15][16][17]) or with weights varying in time according to some adaptation law [18][19][20]. In such cases, a key factor in determining the global behavior of the system is the interplay between its time scales: one related to dynamics of the units, and the other defining the rate of variation of the links between them.…”