No Arabic abstract
Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including electric power networks with renewable energy sources. Such non-Gaussian fluctuations can result in rare network desynchronization. Here we build a general theory for inertial oscillator network desynchronization by non-Gaussian noise. We compute the rate of desynchronization and show that higher-moments of noise enter at specific powers of coupling: either speeding up or slowing down the rate exponentially depending on how noise statistics match the statistics of a networks slowest mode. Finally, we use our theory to introduce a technique that drastically reduces the effective description of network desynchronization. Most interestingly, when instability is associated with a single edge, the reduction is to one stochastic oscillator.
Stochastic feed-in of fluctuating renewable energies is steadily increasing in modern electricity grids and this becomes an important risk factor for maintaining power grid stability. Here we study the impact of wind power feed-in on the short-term frequency fluctuations in power grids based on an IEEE test grid structure, the swing equation for the dynamics of voltage phase angles, and a series of measured wind speed data. External control measures are accounted for by adjusting the grid state to the average power feed-in on a time scale of one minute. The wind power is injected at a single node by replacing one of the conventional generator nodes in the test grid by a wind farm. We determine histograms of local frequencies for a large number of one-minute wind speed sequences taken from the measured data and for different injection nodes. These histograms exhibit a common type of shape, which can be described by a Gaussian distribution for small frequencies and a nearly exponentially decaying tail part. Non-Gaussian features become particularly pronounced for wind power injection at locations, which are weakly connected to the main grid structure. This effect is only present when taking into account the heterogeneities in transmission line and node properties of the grid, while it disappears upon homogenizing of these features. The standard deviation of the frequency fluctuations increases linearly with the average injected wind power.
Traffic is essential for many dynamic processes on real networks, such as internet and urban traffic systems. The transport efficiency of the traffic system can be improved by taking full advantage of the resources in the system. In this paper, we propose a dual-strategy routing model for network traffic system, to realize the plenary utility of the whole network. The packets are delivered according to different efficient routing strategies [Yan, et al, Phys. Rev. E 73, 046108 (2006)]. We introduce the accumulate rate of packets, {eta} to measure the performance of traffic system in the congested phase, and propose the so-called equivalent generation rate of packet to analyze the jamming processes. From analytical and numerical results, we find that, for suitable selection of strategies, the dual- strategy system performs better than the single-strategy system in a broad region of strategy mixing ratio. The analytical solution to the jamming processes is verified by estimating the number of jammed nodes, which coincides well with the result from simulation.
We examine analytically and numerically a variant of the stochastic Kuramoto model for phase oscillators coupled on a general network. Two populations of phased oscillators are considered, labelled `Blue and `Red, each with their respective networks, internal and external couplings, natural frequencies, and frustration parameters in the dynamical interactions of the phases. We disentagle the different ways that additive Gaussian noise may influence the dynamics by applying it separately on zero modes or normal modes corresponding to a Laplacian decomposition for the sub-graphs for Blue and Red. Under the linearisation ansatz that the oscillators of each respective network remain relatively phase-sychronised centroids or clusters, we are able to obtain simple closed-form expressions using the Fokker-Planck approach for the dynamics of the average angle of the two centroids. In some cases, this leads to subtle effects of metastability that we may analytically describe using the theory of ratchet potentials. These considerations are extended to a regime where one of the populations has fragmented in two. The analytic expressions we derive largely predict the dynamics of the non-linear system seen in numerical simulation. In particular, we find that noise acting on a more tightly coupled population allows for improved synchronisation of the other population where deterministically it is fragmented.
We report the study of sudden transitions or tipping in a collection of systems induced due to multiplexing with another network of systems. The emergent dynamics of oscillators on one layer can undergo a sudden transition to steady state due to indirect coupling with a shared environment, mean field couplings and conjugate couplings among them. In all these cases, when multiplexed with another set of similar systems, the tipping phenomena are induced on the second layer also with a similar pattern of behaviour. We consider van der Pol oscillator as nodal dynamics with various network topologies like scale free and regular networks with local and nonlocal couplings. We also report how the coupling topology influences the nature of transitions on both layers, under multiplexing.
A universal approach is proposed for suppression of collective synchrony in a large population of interacting rhythmic units. We demonstrate that provided that the internal coupling is weak, stabilization of overall oscillations with vanishing stimulation leads to desynchronization in a large ensemble of coupled oscillators, without altering significantly the essential nature of each constituent oscillator. We expect our findings to be a starting point for the issue of destroying undesired synchronization, e. g. desynchronization techniques for deep brain stimulation for neurological diseases characterized by pathological neural synchronization.