Propagation patterns unravelled

Timme, Marc; Nagler, Jan

doi:10.1038/s41567-019-0424-9

Cited by 6 publications

(6 citation statements)

References 4 publications

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“…Recently, Hens et al have investigated [10] the spatiotemporal propagation pattern of perturbed signals, i.e how many times a neighbor node of i will take to respond if i is permanently perturbed? Based on the same theory described above, it has been shown that joint contributions of the interaction structure and local dynamics can be disentangled from three specific classes (called as degree driven, distance driven and composite) characterized by the interplay between network paths, degree distribution, and the interaction dynamics [10,408,409]. The individual response time τ q , capture the transient response of the node q to direct incoming perturbations from its interacting neighbors.…”

Section: Spatiotemporal Signal Propagationmentioning

confidence: 99%

Signal propagation in complex networks

et al. 2023

Physics Reports

140

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Section: Spatiotemporal Signal Propagationmentioning

confidence: 99%

Signal propagation in complex networks

et al. 2023

Physics Reports

140

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“…walk processes allows predictions of the arrival times of the perturbation [1,3,4,15,16]. For other spreading processes the total impact of the perturbation at a given unit or the maximal deviation from the operating point is of interest [12,13,[17][18][19][20]. Interestingly, even for the simple deterministic linear system dx/dt = M x described above, these measures cannot be easily evaluated analytically.…”

Section: Perturbations In Network Dynamical Systemsmentioning

confidence: 99%

“…These systems generically operate near a fixed point and are naturally subject to perturbations, for example an outbreak of an infection or fluctuations of the power consumption and production [11]. In their simplest setting, such perturbations initially affect only a single unit and spread through the network, transiently affecting other units at different times and with different strengths [12,13].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Perturbation Spreading in Networks

Schröder

Zhang

Wolter

et al. 2020

IEEE Trans. Netw. Sci. Eng.

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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.

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“…A fundamental issue in the study of collective dynamics is to unravel the complex relation between interactions and dynamics, specially for functionally meaningful trajectories, i.e. having non-trivial spatio-temporal profiles [20,31]. In most natural systems, the precise network structure is unknown and information about the connectivity is obtained indirectly from activity measurement [26].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for signal propagation along an excitable transmission line

Tonnelier

2024

Phys. Rev. E

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show abstract

Propagation patterns unravelled

Cited by 6 publications

References 4 publications

Signal propagation in complex networks

Signal propagation in complex networks

Dynamic Perturbation Spreading in Networks

Exact solutions for signal propagation along an excitable transmission line

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