# Temporal profiles of avalanches on networks

@article{Gleeson2017TemporalPO, title={Temporal profiles of avalanches on networks}, author={James P. Gleeson and Richard Durrett}, journal={Nature Communications}, year={2017}, volume={8} }

An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche shapes, i.e., the temporal profiles of avalanches of fixed duration. At the critical point of the dynamics, the rescaled average avalanche shapes for different durations collapse onto a single universal curve. We apply Markov branching process theory to derive… Expand

#### 33 Citations

Avalanches in a short-memory excitable network

- Advances in Applied Probability
- 2021

Abstract We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced by Larremore et al. (Phys. Rev. E, 2012) and is mathematically… Expand

Field-theoretic approach to the universality of branching processes

- Physics, Mathematics
- Physical Review E
- 2018

Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of… Expand

Avalanches in an excitable network

- Mathematics, Physics
- 2019

We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced in [23], and is mathematically equivalent to an endemic variation of the… Expand

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ–oscillations

- Biology, Physics
- 2019

It is suggested that oscillations provide a transient regularity in an otherwise scale-invariant temporal organization pervading cortical activity at numerous scales, as well as avalanches and oscillations as dual principles in the temporal organization of brain activity. Expand

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ–oscillations

- Medicine, Physics
- Scientific Reports
- 2019

It is shown in awake nonhuman primates that the temporal profile of avalanches follows a symmetrical, inverted parabola spanning up to hundreds of milliseconds, which constrains how avalanches initiate locally, extend spatially and shrink as they evolve in time. Expand

Emergence of power laws in noncritical neuronal systems

- Computer Science, Medicine
- Physical review. E
- 2019

A simplistic model of neuronal dynamics on networks is considered and it is shown that the degree distribution of the underlying neuronal network may trigger power-law distributions for neuronal avalanches even when the system is not in its critical regime. Expand

Unifying criticality and the neutral theory of neural avalanches.

- Physics, Biology
- 2019

It is shown that the neutral theory of neural avalanches can be unified with criticality, which requires fine tuning of control parameters, and rule out self-organized criticality. Expand

Pattern phase diagram of spiking neurons on spatial networks.

- Mathematics, Physics
- Physical review. E
- 2019

An abstracted model of neuronal activity via numerical simulation is studied and spatiotemporal pattern formation and criticallike dynamics are reported, visually resembling the surface of a frothing liquid. Expand

Information Spreading on Memory Activity-Driven Temporal Networks

- Computer Science
- Complexity
- 2021

It is found that network memory may suppress and promote the information spreading dynamics, which depends on the degree heterogeneity and fraction of bigots, and a Markovian approach is developed to describe the model. Expand

Reentrant phase transitions in threshold driven contagion on multiplex networks

- Computer Science, Medicine
- Physical review. E
- 2019

This work investigates threshold driven contagion on weight heterogeneous multiplex networks and shows that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Expand

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