# Self-sustained activity in a small-world network of excitable neurons.

@article{Roxin2004SelfsustainedAI, title={Self-sustained activity in a small-world network of excitable neurons.}, author={Alex Roxin and Hermann Riecke and Sara A. Solla}, journal={Physical review letters}, year={2004}, volume={92 19}, pages={ 198101 } }

We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities p of directed random connections, a localized transient stimulus results either in self-sustained persistent activity or in a brief transient followed by failure. Averages over the quenched ensemble reveal that the probability of failure changes from 0 to 1 over a narrow range in p; this failure transition can be described analytically through an extension of an existing mean-field result…

## 257 Citations

Emergence of self-sustained patterns in small-world excitable media.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

Two distinct dynamical transitions in the activity of excitable media where waves propagate both between neighboring regions and through LRCs are observed, resulting in a spatially homogeneous, temporally periodic state.

Self-sustained non-periodic activity in networks of spiking neurons: The contribution of local and long-range connections and dynamic synapses

- Computer Science, MedicineNeuroImage
- 2010

It is concluded that local and long-range connectivity and short-term synaptic dynamics are together sufficient to support complex persistent activity in a spiking network model.

Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons.

- Mathematics, BiologyChaos
- 2007

It is found that persistent activity emerges at low density of shortcuts, and that the system undergoes a transition to failure as their density reaches a critical value, with multiple stable periodic attractors below this transition.

Pulse-coupled model of excitable elements on heterogeneous sparse networks

- Mathematics, Biology
- 2017

This work presents a framework to estimate, in the stationary state, the mean firing rate over a long time window and to decompose the global dynamics into average values of the inter-spike-interval of each connectivity group, and provides accurate predictions of these average quantities when the network exhibits high heterogeneity.

Building Blocks of Self-Sustained Activity in a Simple Deterministic Model of Excitable Neural Networks

- Computer Science, MedicineFront. Comput. Neurosci.
- 2012

A simple deterministic excitable model is employed to explore how network-wide activation patterns are shaped by network architecture and results show the dependence of the correlation between the adjacency matrix and the instantaneous co-activation matrix on global network features.

Diverse self-sustained oscillatory patterns and their mechanisms in excitable small-world networks.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

Diverse self-sustained oscillatory patterns and their mechanisms in small-world networks of excitable nodes are studied and the mechanism of emergence and annihilation of synchronizing oscillations is explained using the shortest path length analysis.

Stochastic resonance on excitable small-world networks via a pacemaker.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

The optimal interplay between a localized source of weak rhythmic activity and the response of the whole array demands a delicate balance between the strength of excitation transfer and the effectiveness of the network structure to support it.

Self-Sustained Irregular Activity in 2-D Small-World Networks of Excitatory and Inhibitory Neurons

- Computer Science, MedicineIEEE Transactions on Neural Networks
- 2010

Simulation results show that the 2-D SW neural network can sustain such long-lasting firing behavior by using a smaller number of connections than the random neural network.

Robust emergence of small-world structure in networks of spiking neurons

- Computer Science, MedicineCognitive Neurodynamics
- 2006

Numerical simulations with connected Hindmarsh–Rose neurons are presented in which, starting from random connection distributions, small-world networks evolve as a result of applying an adaptive rewiring rule.

Structure and control of self-sustained target waves in excitable small-world networks.

- Computer Science, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

A dominant phase-advanced driving (DPAD) method, which is generally applicable for analyzing all oscillatory complex networks consisting of nonoscillatory nodes, is proposed to reveal the self-organized structures supporting this type of oscillations.

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