Dynamic perturbation spreading in networks
arXiv:2106.00419 · doi:10.1109/TNSE.2019.2901582
Abstract
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they transiently alter. The maximum state changes at those units and the timings of these changes constitute key characteristics of such transient response dynamics. However, even for linear dynamical systems it is not possible to analytically determine time and amplitude of the maximal response of a unit to a perturbation. Here, we propose to extract approximate peak times and amplitudes from effective expectation values used to characterize the typical time and magnitude of the response of a unit by interpreting the system's response as a probability distribution over time. We derive analytic estimators for the peak response based on these expectation value measures in linearized systems operating close to a stable fixed point. These estimators can be expressed in terms of the inverse of the system's Jacobian. We obtain identical results with different approximations for the response dynamics, indicating that these estimators become exact in the limit of weak coupling. Furthermore, the results suggest that perturbations spread ballistically in networks with diffusive coupling.
15 pages, 7 figures
References in corpus (15)
- Optimal Placement of Virtual Inertia in Power Grids
- Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics
- Dynamic information routing in complex networks
- Optimal Paths in Disordered Complex Networks
- Effective Distances for Epidemics Spreading on Complex Networks
- Global disease spread: statistics and estimation of arrival times
- Critical links and nonlocal rerouting in complex supply networks
- Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices
- Survivability of Deterministic Dynamical Systems
- Network susceptibilities: theory and applications
- Delocalization of Phase Disturbances and the Stability of AC Electricity Grids
- Arrival Time Statistics in Global Disease Spread
- Timing of Transients: Quantifying Reaching Times and Transient Behavior in Complex Systems
- Quantifying Transient Spreading Dynamics on Networks
- Estimating epidemic arrival times using linear spreading theory