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Bursty Human Dynamics

Márton Karsai, Hang-Hyun Jo, Kimmo Kaski

arXiv:1803.02580v1physics.soc-phcs.CYcs.SIphysics.data-an

TL;DR

Bursty human dynamics involves heterogeneous, non-Poissonian event sequences, but understanding it has been limited by scarce multiscale behavioural data and challenging temporal structure. This monograph reviews observations, measures, models, and applications, including priority-queuing mechanisms and consequences for collective dynamics. It concludes that bursty systems require approaches addressing temporal heterogeneity, social connectivity, and the complexity of human behaviour.

  • Problem

    Limited access to large-scale, detailed behavioural data and the difficulty of analysing non-stationary, non-Poissonian temporal patterns constrained quantitative understanding of human dynamics.

  • Method

    The monograph synthesises empirical observations, measurement approaches, theoretical models, and applications for bursty human behaviour across individual and social-network scales.

  • Results

    Bursty human dynamics is characterised by broad inter-event-time distributions, while models such as priority queuing can produce exponential decay or power-law behaviour with an exponential cutoff depending on task-selection parameters.

  • Takeaways & Limitations

    Digital communication data make human burstiness quantitatively accessible, but explaining it requires combining temporal-pattern analysis with models of connected individuals and collective processes.

  • Takeaways & Limitations

    A solely Platonic viewpoint may oversimplify human burstiness by neglecting cognitive, psychological, cultural, socioeconomic, and social-network properties.

Abstract

from arXiv · show

Bursty dynamics is a common temporal property of various complex systems in Nature but it also characterises the dynamics of human actions and interactions. At the phenomenological level it is a feature of all systems that evolve heterogeneously over time by alternating between periods of low and high event frequencies. In such systems, bursts are identified as periods in which the events occur with a rapid pace within a short time-interval while these periods are separated by long periods of time with low frequency of events. As such dynamical patterns occur in a wide range of natural phenomena, their observation, characterisation, and modelling have been a long standing challenge in several fields of research. However, due to some recent developments in communication and data collection techniques it has become possible to follow digital traces of actions and interactions of humans from the individual up to the societal level. This led to several new observations of bursty phenomena in the new but largely unexplored area of human dynamics, which called for the renaissance to study these systems using research concepts and methodologies, including data analytics and modelling. As a result, a large amount of new insight and knowledge as well as innovations have been accumulated in the field, which provided us a timely opportunity to write this brief monograph to make an up-to-date review and summary of the observations, appropriate measures, modelling, and applications of heterogeneous bursty patterns occurring in the dynamics of human behaviour.

1 Introduction

Bursty dynamics consists of alternating high- and low-frequency periods and appears across natural, technological, and human systems. Digital traces have enabled quantitative study of bursty human behaviour from individual actions to societal processes, establishing a broad research area while leaving scope and mechanism questions open.

  • Definition: Bursty behaviour is defined by intermittent increases and decreases in event activity, producing non-Poissonian dynamics with strong temporal heterogeneity across scales.Empirical inter-event distributions can be broad and follow log-normal, Weibull, or power-law forms rather than the exponential form associated with Poissonian dynamics.
  • Examples: Examples span earthquakes, neuronal firing, biological evolution, animal activity, written text, and communication systems, showing burstiness across natural and engineered settings.These patterns can occur at single-unit, mesoscale, or system levels.
  • Data and methods: Digital communication technologies and large-scale data now support quantitative analysis of human behaviour across multiple scales and communication channels.Earlier research was constrained by limited access to detailed behavioural data needed to validate theories and develop quantitative approaches.
  • Bursty human dynamics: Human burstiness has been observed in individual actions and dyadic interactions, including emails, letters, calls, messages, browsing, printing, loans, job submissions, and file transfers.Group-level examples include temporal motifs, demonstrations, revolutions, information cascades, and wars.
  • Applications: Research on bursty human dynamics examines how bursty interactions affect collective processes such as information diffusion, epidemics, and random walks.Data-driven models and random reference systems have been used to study whether bursty interactions enhance or slow globally spreading processes.
  • Scope: The monograph focuses exclusively on heterogeneous temporal patterns directly reflecting human actions or interactions, excluding indirectly related systems such as finance and transportation.The authors also acknowledge that some related articles may have been missed.

2 Measures and characterisations

Human social behaviour is represented as a digitally recorded event sequence and analysed with time-series methods that account for regular or irregular observation timings. Irregular event timings can also be transformed through thresholding or coarse-graining for analysis.

  • Event-sequence representation: Human social behaviour is introduced quantitatively as a time series of observations made sequentially in time, with digitally recorded events represented by timings and observed results.The monograph focuses mainly on discrete timings and generally ignores event duration when it is much shorter than the analysis timescale.
  • Timing structure: Regularly timed observations use fixed intervals, whereas emails and similar behaviours produce temporally inhomogeneous time series through irregular event timings.Irregularity can involve both event timing and variation in observed values.
  • Transformations: A regular-valued series can be converted into an irregular event sequence by retaining observations above a threshold, while irregular events can be aggregated into regular intervals.The latter transformation constitutes coarse-graining of the time series.

2.1 Point processes as time series with irregular timings

Point-process representations isolate event timings and use Poisson processes as reference models for characterising bursty sequences. Inter-event distributions, burstiness, correlations, and train-size statistics provide complementary measures, but fitting and finite-size effects complicate interpretation.

  • Point-process representation: An irregularly timed series can be represented as a point process containing ordered event timings, while the observation values may be discarded when unavailable or unnecessary.The event sequence can be formalised using event times and Dirac or Kronecker delta representations.
  • Reference dynamics: Poisson processes provide independent-event reference dynamics, with homogeneous rate λ or time-varying rate λ(t), against which temporal heterogeneity and correlations are assessed.Deviations from Poisson behaviour indicate dynamics unlike independent events with a single exponential timescale.
  • Inter-event distributions: Broad heavy-tailed inter-event distributions distinguish bursty sequences from exponential Poisson distributions, with power-law forms indicating scale-free temporal fluctuations.In P(τ) ∝ τ^-α exp(-τ/τc), α is the power-law exponent and τc sets the exponential cutoff.
  • Burstiness measures: The burstiness parameter B summarizes temporal heterogeneity from the coefficient of variation, with B = 0 for Poissonian series, B > 0 for more heterogeneous series, and B = -1 for regular series.Its simplicity has supported applications including earthquake and heartbeat analysis.
  • Finite-size effects: The burstiness parameter is strongly affected by event count n, so finite-size effects can distort comparisons for sequences with moderate numbers of events.For extremely bursty sequences, B = 1 is reached only as n →∞; a modified measure was proposed to distinguish finite-size effects from intrinsic burstiness.
  • Correlated bursts: Power-law bursty-train sizes across a wide range of Δt indicate correlations between inter-event times and are described as correlated bursts [145].The train size E groups events separated by τ ≤ Δt, while different trains are separated by τ > Δt.

2.2 Inter-event time, residual time, and waiting time

Inter-event time, residual time, and waiting time describe different temporal quantities in bursty systems. Their distinctions matter because random observation creates a waiting-time paradox, while task waiting times need not indicate bursty event dynamics.

  • Definitions: Inter-event time τ is the interval between consecutive events, whereas residual time τr runs from a random observation moment to the next event.The distinction arises because observations cover a finite period that may begin between events.
  • Residual time: The waiting-time paradox shows that the average residual time can exceed the corresponding Poisson reference, with the normalized ratio also serving as a burstiness measure.The ratio can be expressed through the inter-event-time standard deviation and burstiness parameter B.
  • Waiting time: Waiting time τw is the interval a newly arrived task waits before execution, such as the time from manuscript submission to editorial decision.A heavy-tailed P(τw) indicates heterogeneity in task processing but not necessarily bursty dynamics of the underlying process.
  • Relations: For directed interactions such as email responses, waiting-time and inter-event-time distributions can be closely related and may share the same exponent under heterogeneous processes [70].This relation applies to the specific interaction setting rather than defining waiting time generally.

2.3 Collective bursty phenomena

Collective bursty phenomena connect individual interaction sequences to egocentric, contextual, and whole-network dynamics, revealing relationships across these levels.

  • Temporal-network analysis treats social interactions as time-varying event sequences, enabling burstiness to be studied beyond isolated individuals.
  • Bursty patterns in egocentric networks: Ego-level analysis separates collective inter-event times across all contexts from contextual inter-event times involving one neighbour or group.For an ego i, τ(i) spans consecutive events from any context, whereas τ(i,j) spans consecutive events within the same context.
  • Bursty patterns in egocentric networks: Contextual inter-event times can contain multiple collective intervals, providing a basis for scaling relations between their distributions and exponents.For uncorrelated inter-event times, analytical and numerical work relates the power-law exponents α′, α, and η.
  • Bursty patterns in egocentric networks: Ego-level and relationship-level temporal statistics can share similar properties under a stated condition, while forum-level analysis relates individual burstiness to collective burstiness.
  • Scaling relations: Scaling relations link temporal interaction parameters with structural distributions such as node degree and link weight across human-interaction datasets.The relations use sociability κ, inter-event-time exponents, average parameters, and variability in sociability u, and are supported with scaling functions.
  • Whole-network burstiness: Temporal motifs identify ordered interaction patterns, while temporal-network sparsity ζtemp measures event heterogeneity and has explanatory power for spreading dynamics.Lower ζtemp indicates more severe temporal heterogeneity and a more temporally sparse network.

2.4 Cyclic patterns in human dynamics

Human activity contains circadian, weekly, and longer cycles that contribute to temporal heterogeneity, so deseasoning is used to separate cyclic effects from other burstiness.

  • Cyclic patterns: Circadian, weekly, and longer cycles contribute to temporal inhomogeneity, producing periodic structure in human event sequences.Peaks in inter-event-time distributions can correspond to multiples of one day in mobile-phone calls and blog posts.
  • Deseasoning: Deseasoning identifies a period-specific event rate, extends it periodically, and transforms time so the deseasoned event rate becomes uniform.The transformation uses ρ(t)dt = ρ*(t*)dt* and ρ*(t*) = 1.
  • Deseasoning: The method dilates time during high event rates and contracts it during low rates, then compares deseasoned and original sequences to test whether cycles explain temporal heterogeneity.
  • Deseasoning: For mobile-phone calls, original and deseasoned inter-event-time distributions had almost the same shape across several periods, indicating other origins of human burstiness beyond circadian and weekly cycles.
  • Aggregated and ordinal time frames: Deseasoning extends to aggregated activity groups and can reach an ordinal time frame in which event order replaces real timing.With full deseasoning, contextual intervals count intervening events from other contexts rather than elapsed clock time.
  • Remark on non-stationarity: Because bursty phenomena can be scale-free and hierarchical, stationarity assumptions may hold only over restricted time scales, motivating deseasoning and related detrending methods.

3 Empirical findings in human bursty dynamics

Empirical studies find bursty human dynamics across individual activities, social interactions, financial systems, and mobility, but the observed distributions and exponents vary with phenomenon, activity level, and observation scale.

  • Individual activities and interactions: Heavy-tailed or power-law inter-event distributions recur across individual activities, face-to-face interactions, mobile communications, financial transactions, and human mobility.Other datasets are better described by stretched-exponential, Weibull, log-normal, or bimodal forms, indicating heterogeneous mechanisms.
  • Mobile phone-based interactions: Call sequences have α ≈ 0.7, whereas SMS sequences have α = 1.0, and normalized distributions collapse across activity groups.The collapse implies strong similarity in human behaviour across different activity levels.
  • Mobile phone-based interactions: More than 73% of mobile-phone users show Weibull inter-event distributions even when aggregate activity follows a power law [121].Among users in the power-law group, α ranges from 1.5 to 2.6 [121].
  • Mobile phone-based interactions: Bursty patterns remain robust after deseasoning circadian and weekly cycles in mobile calls and SMSs [125].This result addresses whether periodic human routines account for the observed burstiness.
  • Individual activities and interactions: Power-law exponents range from 0.2 to 2.5 across human activities, and more active Netflix users show larger α values, indicating less bursty patterns [311].The reported dependence on activity level and observation scale argues against a single universal exponent.
  • Human mobility: Human mobility is bursty in both time and space because high-resolution trajectories reveal heavy-tailed staying or displacement intervals, sometimes with power-law tails.The inter-event time represents either staying in a location or the interval between consecutive displacements.

4 Models and mechanisms of bursty behaviour

Bursty human dynamics has been observed at individual, dyadic, and network levels, motivating models that capture phenomena across multiple scales despite sometimes conflicting interpretations.

  • Models and mechanisms of bursty behaviour: Models of bursty behaviour address individual activities, dyadic interactions, and collective network phenomena across multiple scales.The chapter presents these efforts comprehensively so readers can assess their differing interpretations.

4.1 Models of individual activity

Individual-activity models explain bursty waiting and inter-event times through task prioritisation, activity-rate heterogeneity, memory, state switching, or fitted cascades. These mechanisms can produce power-law behavior, but descriptive and independent models have important explanatory limits.

  • Cobham priority queuing model: αw = 3/2 at ρ = 1, with an exponential cutoff; for ρ > 1, a fraction 1−ρ^-1 of tasks remains in the queue forever.The queue length behaves as a bounded random walk when ρ = 1, producing the 3/2 exponent; when ρ > 1, the average queue length grows linearly.
  • Barabási priority queuing model: Barabási’s priority model produces exponential waiting times at p = 0 and a power law with an exponential cutoff as p →1.The cutoff shifts toward larger τw values as p increases, while relaxation becomes slower and eventually non-stationary near p = 1.
  • Position based priority lists: Priority-list models generate tunable power-law inter-event exponents α ∈[1,2], while finite lists add an exponential cutoff that disappears as l →∞.The exponent depends on the priority distribution, including power-law, exponential, and stretched-exponential forms.
  • Processes with simple memory functions: Simple-memory processes produce power-law inter-event distributions in accelerating regimes, with α = 2 + 1/(a −1) when τ0 ≪τ < T.For 1/2 < a < 1, no power-law scaling appears, whereas 0 < a < 1/2 yields another power-law regime.
  • Bursty model with Poissonian cascades: Poissonian-cascade models closely match empirical individual inter-event distributions by combining inactive periods, active states, and fitted activity parameters.The model uses parameters for weekly and daily activity, within-active-period rates, and cascade sizes inferred through simulated annealing.
  • Other type of models: Independent sampling reproduces heterogeneous activity but neither explains burst origins nor induces correlations between consecutive events.Such models have been used to study spreading in temporal networks and to identify spurious autocorrelation from heterogeneous independent signals.

4.2 Models of link activity

Link-activity models explain bursty interaction patterns by coupling agents’ priority-driven task execution with interaction protocols. These models show how protocol choice and competing tasks shape inter-event-time distributions.

  • 4.2.1 Interacting priority queues: Interacting priority queues model two agents whose shared task is executed only when both select it, while other tasks are executed separately.The resulting inter-event-time exponent depends on queue length, with α = 1 + 1/max{l_j − 1}.
  • 4.2.1 Interacting priority queues: The AND protocol can produce frozen states in networks, motivating an OR protocol for interactions that one participant can initiate, such as phone calls or instant messages.The OR protocol is presented as more suitable when simultaneous action is not required from both agents.
  • 4.2.2 Combined Poissonian and priority-induced bursts: A combined model attributes the bimodal inter-event-time distribution of SMS communications to Poissonian burst initiation, individual task competition, and interactions.It therefore combines processes operating at different time scales.
  • 4.2.2 Combined Poissonian and priority-induced bursts: The interacting-queue framework introduces ranked task execution and processing times to represent how two individuals’ task lists generate interaction dynamics.Tasks are executed probabilistically according to priority, while processing time sets the scale for task execution and insertion.

4.3 Network models of bursty agents

Network models extend bursty-agent dynamics to systems where temporal activity and network structure evolve together. They reproduce heavy-tailed interactions, scale-free topology, ageing, and phase behavior arising from burstiness and tie reinforcement.

  • Zero-crossing model: The zero-crossing model couples bloggers’ random walks to posting and commenting, producing both bursty posting times and evolving blog-network structure.Its posts are generated whenever a walker returns to the origin, with posts becoming new conversations or comments.
  • Zero-crossing model: The simulated blog network has power-law in-degree and cascade-size distributions, while blogger inter-event times follow P(τ) ∼ τ^-3/2 and activity signals have fractal dimension 0.5.These results are comparable to the empirical observations discussed by the authors.
  • Reinforcement-based contact networks: Reinforcement-based group models reproduce power-law interaction and inter-event times and show that group stability decreases as group size increases.Groups evolve through successive mergings and splittings driven by reinforcement processes.
  • Dynamic networks with memory: Memory-based evolving-network models can generate scale-free structure and bursty interactions when the fitness distribution and average degree satisfy the stated parameter relation.With power-law fitness, the model induces a scale-free structure; bursty interactions arise when ⟨x⟩ ≪ ⟨k⟩.
  • Activity-driven models with bursty agents: Renewal-based activity models link degree, waiting-time, and heterogeneity exponents through γ = 1 + β/α and exhibit ageing when α < 1.The relation shows how temporal renewal properties affect emergent network topology.
  • Activity-driven models with bursty agents: Direct burstiness combined with memory-driven tie reinforcement produces a non-trivial phase diagram governed by the relative strengths of the two mechanisms.In these models, burstiness directly affects network evolution rather than emerging from the network dynamics.

5 Dynamical processes on bursty systems

Bursty human interactions affect diffusion, spreading, and other dynamical processes on temporal networks. Existing findings are heterogeneous, so the review organizes effects by bursty characteristics and process type rather than proposing a closed theory.

  • 5 Dynamical processes on bursty systems: Bursty interaction patterns matter because they affect random walks, information diffusion, epidemics, social contagion, and evolutionary games on networks.Earlier studies often treated these processes as occurring on static structures.
  • 5 Dynamical processes on bursty systems: Data-driven simulations and theoretical analyses found that burstiness can slow the emergence of several dynamical processes.These observations created a central puzzle about how temporal heterogeneity changes process dynamics.
  • 5 Dynamical processes on bursty systems: The effects of bursty interactions depend strongly on the dataset and dynamical model, leaving some questions open for further research.The review therefore discusses bursty characteristics first and then findings for different process types rather than offering a closed theory.

5.1 Bursty characteristics controlling dynamical processes

The effects of burstiness are controlled by inter-event-time heterogeneity, residual waiting times, and event ordering. These quantities determine how quickly walkers and spreading processes can traverse temporal networks.

  • Random reference models: Shuffling event times in random reference models removes temporal correlations and bursty patterns, enabling comparisons between original and temporally randomized interaction sequences.This procedure assigns events random times within the observation window while preserving the event sequence’s other selected properties.
  • The waiting-time paradox: Broad inter-event-time distributions create longer residual waiting times than Poissonian dynamics, with power-law tails related by P(τr) ∼ τr^−(α−1).For α ≤ 3, the diverging second moment makes the mean residual time diverge.
  • The waiting-time paradox: Residual waiting time depends on the first and second moments of inter-event times, so larger rate fluctuations increase delay relative to regular interactions.A Poisson process already has twice the mean residual time of a perfectly regular process, while broader distributions increase the deviation further.
  • Ordering of events: For random walks, relative residual-time distributions on neighboring links matter, whereas spreading additionally depends on residual times relative to recovery times.Thus both temporal heterogeneity and event ordering affect dynamical outcomes.
  • Ordering of events: Low-activity bursty ties positioned as bridges between communities can keep spreading localized within highly connected communities with active links.Their network position makes the timing of interactions especially consequential for final spreading outcomes.

Early and late time effects of burstiness

Bursty inter-event times can accelerate spreading at early times but slow its late-time progression, because short and long waiting times dominate different regimes.

  • Model formulation: The spreading framework uses arbitrary inter-event distributions and residual waiting times to calculate infection dynamics from renewal-process interactions.Generating functions and Laplace transforms allow Poissonian and non-Poissonian cases to be evaluated within the same formulation.
  • Early time effects: Non-Poissonian burstiness generally accelerates early-time spreading relative to a shifted Poissonian process with the same mean and lower-bound inter-event times.The effect is attributed to small inter-event times and is supported by numerical studies of SI processes.
  • Late time effects: At late times, heterogeneous activity slows spreading, with prevalence decaying according to the same exponent as the generation-time distribution in the stable Lévy regime.For g(Δ) ∼ Δ^-ν with 1 < ν < 2, the long-time convolution scales as t^-ν independently of network structure.
  • Renewal and non-stationary dynamics: The same early-versus-late contrast appears in renewal-process models: burstiness accelerates initial SI growth but slows the later dynamics compared with Poissonian interaction patterns.Numerical studies confirm the late-time slowing, while non-stationary power-law processes can produce especially rapid early spreading.

5.1.2 Triggered event correlations

Triggered correlations between temporal-network events can shorten relay times and alter spreading, with their effect depending on recovery times and the process being studied.

  • Triggered relay times: Increasing triggered-event probability shortens the mean relay time between neighboring links, indicating faster information spreading than with independent events.When p = 0, the mean relay time equals the mean residual time; for p > 0, more triggered events reduce it.
  • SIR spreading: In mobile-phone SIR data, causally correlated neighboring-link events increase transmissibility and epidemic-cascade size for small infection rates.The real interaction sequences contain more post-incoming-call events than time-shuffled sequences.
  • SIR spreading: For sufficiently large recovery times, burstier real communication sequences instead produce smaller spreading cascades because their inter-event-time tails are heavier than exponential tails.The heavier tail increases the probability that no event occurs during the recovery interval.
  • Random walks: Temporal correlations can also slow random-walk exploration, producing longer mean first-passage times than mean-field Poissonian dynamics.Face-to-face interaction sequences exhibit temporal correlations between consecutive conversations associated with this slowing.

5.1.3 Effects of link burstiness

Link burstiness affects spreading and diffusion through temporal heterogeneity, link lifetimes, repeated contacts, and structural-temporal correlations, whose relative dominance is dataset-dependent.

  • Link dynamics: Separating burstiness from link lifetime requires null models because studies distinguish an ongoing-link picture from a link-turnover picture within a finite observation window.Holme and Liljeros examined whether precise bursty timing or link lifespan matters more for SIR and SIS outcomes.
  • Random walks: Empirical greedy random walks often remain within small node sets because non-Markovian repeated-contact patterns reduce network coverage relative to a temporal reference model.The process is particularly sensitive to temporal-topological patterns involving repeated contacts.
  • Other bursty characters: Lower temporal sparsity corresponds to more heterogeneous bursty patterns and a smaller spreading slow-down coefficient in empirical temporal networks.Spreading velocity is strongly correlated with temporal sparsity, linking system-level heterogeneity to SI dynamics.
  • Dominant characters: Random-reference analyses identify temporal heterogeneity as the dominant control on epidemic-spreading speed, accelerating early spreading but slowing later dynamics relative to Poissonian systems.Triggered correlations are less dominant for early spreading, whereas weight-topology correlations can enhance spreading when highly active links lie inside communities.
  • Temporal versus structural effects: Diffusion mixing can be dominated either by temporal inhomogeneity or structural properties, depending on the waiting-time distribution and the spectral gap of the interaction matrix.The framework represents node states with x_i, interaction structure with L, and temporal evolution through waiting-time statistics such as mean, variance, and cutoff.

5.2 Dynamical processes on bursty temporal networks

Bursty temporal heterogeneity changes how epidemic spreading, random walks, evolutionary games, and other dynamical processes unfold on temporal networks. Across these processes, waiting times, memory, repeated interactions, and temporal connectivity determine outcomes differently from Poissonian or shuffled dynamics.

  • Epidemic spreading: Bursty residual-time tails slow information propagation below the epidemic threshold but can accelerate initial epidemic growth above it.For R0 < 1, spreading depends mainly on the longest residual times; for R0 > 1, the Bellman-Harris model predicts faster-than-expected initial exponential growth.
  • Epidemic spreading: R0 remains usable for locating the epidemic threshold in bursty systems, and its value scales with epidemic speed.The relation between R0 and final outbreak size can nevertheless be violated in temporal networks, where different transmission and recovery parameters may produce the same R0 but different outcomes.
  • Epidemic spreading: Increasing p weakens the slowing-down effect, while burstiness reduces interaction transmissibility and hinders epidemic spreading.At p = 1, the deterministic SI process is recovered; as p approaches zero, the average residual time rather than its tail determines spreading.
  • Random walks: Memory kernels make temporal-network dynamics depend on system states across the entire history rather than only the current state.For passive random walks, heavy-tailed residual times favor returning to the previous node, producing conversation-like trapping and non-Markovian motion; the approximated steady state is nevertheless uniform.
  • Threshold processes and evolutionary games: Burstiness can hinder infection cascades and cooperation because repeated events and increased link waiting times reduce effective temporal transmission.Shuffling interaction times removes burstiness, spreads events more evenly, and can increase temporal paths ending at nodes or improve cooperation.
  • Other dynamical processes: Burst identification and slow dynamics also arise from link-creation bursts and critical Griffiths-phase models, extending bursty-network analysis beyond epidemic and walking processes.Twitter link bursts may be externally induced and associated with more homogeneous interest-based egocentric networks, while Griffiths-phase systems exhibit slow bursty dynamics with power-law interconnection times.

6 Discussion

The monograph reviews bursty human dynamics as heterogeneous, non-Poissonian activity spanning individual actions, social interactions, and collective processes. It combines measures, empirical observations, models, and process-level consequences while emphasizing both mathematical regularities and human-specific contextual variation.

  • Scope and motivation: Bursty human systems alternate between high- and low-frequency activity and cannot be characterized by a single-scale Poisson process.The review frames burstiness as a broad phenomenon across natural and man-made systems, including earthquakes, human interactions, and information diffusion.
  • Scope and motivation: The monograph addresses the challenge of characterizing and modeling bursty human phenomena across individual, dyadic, group, and societal levels.Examples include email correspondence, temporal social networks, demonstrations, revolutions, information cascades, and wars.
  • Characterisation: Chapter 2 assembles measures for inter-event distributions, burstiness, memory, train sizes, autocorrelation, temporal networks, and daily or weekly cycles.These methods are used to detect temporal inhomogeneity, long-range memory, system-level temporal structure, and cyclic effects.
  • Empirical evidence: Chapter 3 systematically reviews empirical observations across individual activities and interaction-driven collective activities, including multiple social-interaction modalities.The review organizes datasets, bursty-character values, and references, with additional examples from mobility, finance, and animal behavior.
  • Modelling: Chapter 4 summarizes priority queuing, reinforcement and memory, Poisson-based, reference, individual, dyadic, and network models of bursty behavior.The models range from single-person activity dynamics to bursty interactions and networks with emergent burstiness.
  • Dynamical consequences: Chapter 5 reviews how heterogeneous timing controls information transmission and temporal connectedness across dynamical processes on bursty interaction networks.It covers inter-event and residual times, event ordering, triggered correlations, node and link burstiness, and their effects on early and late collective dynamics.
  • Future directions and methodological approaches: The review identifies non-stationarity and the balance between abstract regularities and human-specific behavioral variation as important unresolved methodological issues.Circadian rhythms and fat-tailed inter-event distributions can prevent stationarity, while cognitive, psychological, social, and socioeconomic differences motivate complementary methodological viewpoints.
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