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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Recovery time after localized perturbations in complex dynamical networks

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Author(s):
Mitra, Chiranjit [1, 2] ; Kittel, Tim [1, 2] ; Choudhary, Anshul [3] ; Kurths, Juergen [1, 2] ; Donner, Reik V. [2]
Total Authors: 5
Affiliation:
[1] Humboldt Univ, Dept Phys, D-12489 Berlin - Germany
[2] Potsdam Inst Climate Impact Res, Res Domain Transdisciplinary Concepts & Methods 4, D-14473 Potsdam - Germany
[3] Carl von Ossietzky Univ Oldenburg, Theoret Phys Complex Syst, ICBM, D-26111 Oldenburg - Germany
Total Affiliations: 3
Document type: Journal article
Source: NEW JOURNAL OF PHYSICS; v. 19, OCT 4 2017.
Web of Science Citations: 5
Abstract

Maintaining the synchronous motion of dynamical systems interacting on complex networks is often critical to their functionality. However, real-world networked dynamical systems operating synchronously are prone to random perturbations driving the system to arbitrary states within the corresponding basin of attraction, thereby leading to epochs of desynchronized dynamics with a priori unknown durations. Thus, it is highly relevant to have an estimate of the duration of such transient phases before the system returns to synchrony, following a random perturbation to the dynamical state of any particular node of the network. Weaddress this issue here by proposing the framework of single-node recovery time (SNRT) which provides an estimate of the relative time scales underlying the transient dynamics of the nodes of a network during its restoration to synchrony. Weutilize this in differentiating the particularly slow nodes of the network from the relatively fast nodes, thus identifying the critical nodes which when perturbed lead to significantly enlarged recovery time of the system before resuming synchronized operation. Further, we reveal explicit relationships between the SNRT values of a network, and its global relaxation time when starting all the nodes from random initial conditions. Earlier work on relaxation time generally focused on investigating its dependence on macroscopic topological properties of the respective network. However, we employ the proposed concept for deducing microscopic relationships between topological features of nodes and their respective SNRT values. The framework of SNRT is further extended to a measure of resilience of the different nodes of a networked dynamical system. We demonstrate the potential of SNRT in networks of Rossler oscillators on paradigmatic topologies and a model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics illustrating the conceivable practical applicability of the proposed concept. (AU)

FAPESP's process: 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications
Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants