Reentrant transition in coupled noisy oscillators

We report on a novel type of instability observed in a noisy oscillator unidirectionally coupled to a pacemaker. Using a phase oscillator model, we find that, as the coupling strength is increased, the noisy oscillator lags behind the pacemaker more frequently and the phase slip rate increases, which may not be observed in averaged phase models such as the Kuramoto model. Investigation of the corresponding Fokker-Planck equation enables us to obtain the reentrant transition line between the synchronized state and the phase slip state. We verify our theory using the Brusselator model, suggesting that this reentrant transition can be found in a wide range of limit cycle oscillators.Comment: 16 pages, 7 figure

Synchronization Transition of Identical Phase Oscillators in a Directed Small-World Network

We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on the shortcut density and on the asymmetry of the phase coupling function, there exists a regime of persistent chaotic dynamics. By increasing the density of shortcuts or decreasing the asymmetry of the phase coupling function, we observe a discontinuous transition in the ability of the system to synchronize. Using a control technique, we identify the bifurcation scenario of the order parameter. We also discuss the relation between dynamics and topology and remark on the similarity of the synchronization transition to directed percolation.Comment: This article has been accepted in AIP, Chaos. After it is published, it will be found at http://chaos.aip.org/, 12 pages, 9 figures, 1 tabl

Decentralised control of material or traffic flows in networks using phase-synchronisation

We present a self-organising, decentralised control method for material flows in networks. The concept applies to networks where time sharing mechanisms between conflicting flows in nodes are required and where a coordination of these local switches on a system-wide level can improve the performance. We show that, under certain assumptions, the control of nodes can be mapped to a network of phase-oscillators. By synchronising these oscillators, the desired global coordination is achieved. We illustrate the method in the example of traffic signal control for road networks. The proposed concept is flexible, adaptive, robust and decentralised. It can be transferred to other queuing networks such as production systems. Our control approach makes use of simple synchronisation principles found in various biological systems in order to obtain collective behaviour from local interactions

Erosion of synchronization and its prevention among noisy oscillators with simplicial interactions

Previous studies of oscillator populations with two-simplex interaction report novel phenomena such as discontinuous desynchronization transitions and multistability of synchronized states. However, the noise effect has not been well understood. Here, we find that when oscillators with two-simplex interaction alone are subjected to external noise, synchrony is eroded and eventually completely disappears even when the noise is infinitesimally weak. Nonetheless, synchronized states may persist for extended periods, with the lifetime increasing approximately exponentially with the strength of the two-simplex interaction. Assuming weak noise and using Kramers' rate theory, we derive a closed dynamical equation for the Kuramoto order parameter, by which the exponential dependence is derived. Further, when sufficiently strong one-simplex coupling is additionally introduced, noise erosion is prevented and synchronized states become persistent. The bifurcation analysis of the desynchronized state reveals that as one-simplex coupling increases, the synchronized state appears supercritically or subscritically depending on the strength of two-simplex coupling. Our study uncovers the processes of synchronization and desynchronization of oscillator assemblies in higher-order networks and is expected to provide insight into the design and control principles in such systems