Tyloo, Melvyn Sandy | Engineering Papers

DOE OSTI2024

Resilience of the slow component in timescale separated synchronized oscillators

Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems. If the coupling is strong enough compared to the heterogeneity of the internal parameters, synchronized states might emerge where phase oscillators start to behave coherently. Here, we focus on the case where synchronized oscillators are divided into a fast and a slow component so that the two subsets evolve on separated timescales. We assess the resilience of the slow component by, first, reducing the dynamics of the fast one using Mori-Zwanzig formalism. Second, we evaluate the variance of the phase deviations when the oscillators in the two components are subject to noise with possibly distinct correlation times. From the general expression for the variance, we consider specific network structures and show how the noise transmission between the fast and slow components is affected. Interestingly, we find that oscillators that are among the most robust when there is only a single timescale, might become the most vulnerable when the system undergoes a timescale separation. We also find that layered networks seem to be insensitive to such timescale separations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Resilience of the slow component in timescale-separated synchronized oscillators

Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems. If the coupling is strong enough compared to the heterogeneity of the internal parameters, synchronized states might emerge where phase oscillators start to behave coherently. Here, we focus on the case where synchronized oscillators are divided into a fast and a slow component so that the two subsets evolve on separated timescales. We assess the resilience of the slow component by, first, reducing the dynamics of the fast one using Mori-Zwanzig formalism. Second, we evaluate the variance of the phase deviations when the oscillators in the two components are subject to noise with possibly distinct correlation times. From the general expression for the variance, we consider specific network structures and show how the noise transmission between the fast and slow components is affected. Interestingly, we find that oscillators that are among the most robust when there is only a single timescale, might become the most vulnerable when the system undergoes a timescale separation. We also find that layered networks seem to be insensitive to such timescale separations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Locating the Source of Forced Oscillations in Transmission Power Grids

A forced oscillation event in power grids refers to a state where malfunctioning or abnormally operating equipment causes persisting periodic disturbances in the system. While power grids are designed to damp most perturbations during standard operations, some of them can excite normal modes of the system and cause significant energy transfers across the system, creating large oscillations thousands of miles away from the source. Localization of the source of such disturbances remains an outstanding challenge due to a limited knowledge of the system parameters outside of the zone of responsibility of system operators. Here, we propose a new method for locating the source of forced oscillations that addresses this challenge by performing a simultaneous dynamic model identification using a principled maximum likelihood approach. We illustrate the validity of the algorithm on a variety of examples where forcing leads to resonance conditions in the system dynamics. Our results establish that an accurate knowledge of system parameters is not required for a successful inference of the source and frequency of a forced oscillation. We anticipate that our method will find a broader application in general dynamical systems that can be well described by their linearized dynamics over short periods of time.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

More is definitely different: the zebrafish as witness: Comment on ”Structure and function in artificial, zebrafish and human neural networks” by Peng Ji et al.

We report half a century ago, in his foundation paper More is different, Anderson stated the relevance of including multiple scales of interaction, instead of trying to reduce everything to fundamental principles. By doing so, one may witness phenomena that were not expected by looking at each individual components separately. This idea finds indeed numerous realizations such as the synchronization phenomenon, where a multitude of dynamical systems suddenly start to behave coherently together, or the spreading of diseases over entire populations, to name only two examples. But if one would have to give a single example of a system where the multiplicity of interaction scales is of utmost importance, it would probably be the brain. In their review, Ji et al. give a comprehensive overview of the multiple scales of science required in the investigation of structural and functional brain networks, as well as their interplay.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Faster network disruption from layered oscillatory dynamics

Nonlinear complex network-coupled systems typically have multiple stable equilibrium states. Following perturbations or due to ambient noise, the system is pushed away from its initial equilibrium, and, depending on the direction and the amplitude of the excursion, it might undergo a transition to another equilibrium. It was recently demonstrated [M. Tyloo, J. Phys. Complex. 3 03LT01 (2022)] that layered complex networks may exhibit amplified fluctuations. Here, I investigate how noise with system-specific correlations impacts the first escape time of nonlinearly coupled oscillators. Interestingly, I show that, not only the strong amplification of the fluctuations is a threat to the good functioning of the network but also the spatial and temporal correlations of the noise along the lowest-lying eigenmodes of the Laplacian matrix. Finally, I analyze first escape times on synthetic networks and compare noise originating from layered dynamics to uncorrelated noise.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Propagation of non-Gaussian voltage angle fluctuations in high-voltage power grids

Recent measurements have reported non-Gaussian tails in the distribution of frequency data in electric power grids. Large frequency deviations may induce grid instabilities and it is therefore crucial to understand how noise disturbances with long, non-Gaussian tails propagate. Here, we investigate how fluctuations in power feed-in, characterized by non-zero cumulants of their distribution, propagate through high-voltage power grids. Unlike previous investigations which focused on the white-noise limit, we consider the limit of long noise correlation time, where power feed-in fluctuates over times longer than the inherent dynamical time scales of the grid - the relevant regime for large-scale, high-voltage distribution grids. In this work, we show that in this limit, the skewness and kurtosis of the power feed-in distribution propagate similarly as its variance, independently of the distribution of inertia. Non-Gaussianities from individual sources of noise therefore persist throughout the entire network. This finding is corroborated by numerical results on a realistic model of the synchronous grid of continental Europe.

42 ENGINEERING↗

DOE OSTI2022

Locating fast-varying line disturbances with the frequency mismatch

In an attempt to provide an efficient method for line disturbance identification in complex networks of diffusively coupled agents, we recently proposed to leverage the frequency mismatch. The frequency mismatch filters out the intricate combination of interactions induced by the network structure and quantifies to what extent the trajectory of each agent is affected by the disturbance. In this previous work, we provided some analytical evidence of its efficiency when the perturbation is assumed to be slow. Here we claim that the frequency mismatch performs actually well for most disturbance regimes. This is shown through a series of simulations and is backed up by an analytical argument. Therefore, we argue that the frequency mismatch is an efficient and elegant tool for line disturbance location in complex networks of diffusively coupled agents.

97 MATHEMATICS AND COMPUTING↗