Francis J. Doyle

Yongqiang Wang, Francis J. Doyle · meta-ai

The exponential synchronization rate is addressed for Kuramoto oscillators in the presence of a pacemaker. When natural frequencies are identical, we prove that synchronization can be ensured even when the phases are not constrained in an open half-circle, which improves the existing results in the literature. We derive a lower bound on the exponential synchronization rate, which is proven to be an increasing function of pacemaker strength, but may be an increasing or decreasing function of local coupling strength. A similar conclusion is obtained for phase locking when the natural frequencies are non-identical. An approach to trapping phase differences in an arbitrary interval is also given, which ensures synchronization in the sense that synchronization error can be reduced to an arbitrary level.

Yongqiang Wang, Felipe Nunez, Francis J. Doyle · meta-ai

This paper addresses the synchronization rate of weakly connected pulse-coupled oscillators (PCOs). We prove that besides coupling strength, the phase response function is also a determinant of synchronization rate. Inspired by the result, we propose to increase the synchronization rate of PCOs by designing the phase response function. This has important significance in PCO-based clock synchronization of wireless networks. By designing the phase response function, synchronization rate is increased even under a fixed transmission power. Given that energy consumption in synchronization is determined by the product of synchronization time and transformation power, the new strategy reduces energy consumption in clock synchronization. QualNet experiments confirm the theoretical results.

Yongqiang Wang, Yutaka Hori, Shinji Hara et al. · meta-ai

Many biological oscillators are arranged in networks composed of many inter-coupled cellular oscillators. However, results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from the oscillation period of an autonomous cellular oscillator. Based on the Goodwin oscillator, we analyze the collective oscillation pattern of coupled cellular oscillator networks. 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 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. Simulation results are given to confirm the theoretical predictions.

Lukas Ortmann, Dawei Shi, Eyal Dassau et al.

The insulin sensitivity (IS) of the human body changes with a circadian rhythm. This adds to the time-varying feature of the glucose metabolism process and places challenges on the blood glucose (BG) control of patients with Type 1 Diabetes Mellitus. This paper presents a Model Predictive Controller that takes the periodic IS into account, in order to enhance BG control. The future effect of the IS is predicted using a machine learning technique, namely, a customized Gaussian Process (GP), based on historical training data. The training data for the GP is continuously updated during closed-loop control, which enables the control scheme to learn and adapt to intra-individual and inter-individual changes of the circadian IS rhythm. The necessary state information is provided by an Unscented Kalman Filter. The closed-loop performance of the proposed control scheme is evaluated for different scenarios (including fasting, announced meals and skipped meals) through in silico studies on simulation models of Göttingen Minipigs.