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

Application of High-precision Timing Systems to Distributed Survey Systems

In any hydrographic survey system that consists of more than one computer, one of the most difficult integration problems is to ensure that all components maintain a coherent sense of time. Since virtually all modern survey systems are of this type, timekeeping and synchronized timestamping of data as it is created is of significant concern. This paper describes a method for resolving this problem based on the IEEE 1588 Precise Time Protocol (PTP) implemented by hardware devices, layered with some custom software called the Software Grandmaster (SWGM) algorithm. This combination of hardware and software maintains a coherent sense of time between multiple ethernet-connected computers, on the order of 100 ns (rms) in the best case, of the timebase established by the local GPS-receiver clock. We illustrate the performance of this techniques in a practical survey system using a Reson 7P sonar processor connected to a Reson 7125 Multibeam Echosounder (MBES), integrated with an Applanix POS/MV 320 V4 and a conventional data capture computer. Using the timing capabilities of the PTP hardware implementations, we show that the timepieces achieve mean (hardware based) synchronization and timestamping within 100-150 ns (rms), and that the data created at the Reson 7P without hardware timestamps has a latency variability of 28 µs (rms) due to software constraints within the capture system. This compares to 288 ms (rms) using Reson’s standard hybrid hardware/software solution, and 13.6 ms (rms) using a conventional single-oscillator timestamping model

Collective oscillation period of inter-coupled biological negative cyclic feedback oscillators

A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from that of an autonomous oscillator. Based on cyclic feedback oscillators, we analyze the collective oscillation pattern of coupled cellular oscillators. First we give a condition under which the oscillator network exhibits oscillatory and synchronized behavior. Then we estimate the collective oscillation period based on a novel multivariable harmonic balance technique. Analytical results are derived in terms of biochemical parameters, thus giving insight into the basic mechanism of biological oscillation and providing guidance in synthetic biology design.Comment: arXiv admin note: substantial text overlap with arXiv:1203.125