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

Design Principles of Pancreatic Islets: Glucose-dependent Coordination of Hormone Pulses

Pancreatic islets are functional units involved in glucose homeostasis. The multicellular system comprises three main cell types; $\beta$ and $\alpha$ cells reciprocally decrease and increase blood glucose by producing insulin and glucagon pulses, while the role of $\delta$ cells is less clear. Although their spatial organization and the paracrine/autocrine interactions between them have been extensively studied, the functional implications of the design principles are still lacking. In this study, we formulated a mathematical model that integrates the pulsatility of hormone secretion and the interactions and organization of islet cells and examined the effects of different cellular compositions and organizations in mouse and human islets. A common feature of both species was that islet cells produced synchronous hormone pulses under low- and high- glucose conditions, while they produced asynchronous hormone pulses under normal glucose conditions. However, the synchronous coordination of insulin and glucagon pulses at low glucose was more pronounced in human islets that had more $\alpha$ cells. When $\beta$ cells were selectively removed to mimic diabetic conditions, the anti-synchronicity of insulin and glucagon pulses was deteriorated at high glucose, but it could be partially recovered when the re-aggregation of remaining cells was considered. Finally, the third cell type, $\delta$ cells, which introduced additional complexity in the multicellular system, prevented the excessive synchronization of hormone pulses. Our computational study suggests that controllable synchronization is a design principle of pancreatic islets.Comment: 24 pages, 7 figure