Splay States in Finite Pulse-Coupled Networks of Excitable Neurons

@article{Dipoppa2012SplaySI,
  title={Splay States in Finite Pulse-Coupled Networks of Excitable Neurons},
  author={Mario Dipoppa and Martin Krupa and Alessandro Torcini and Boris S. Gutkin},
  journal={SIAM J. Appl. Dyn. Syst.},
  year={2012},
  volume={11},
  pages={864-894}
}
The emergence and stability of splay states is studied in fully coupled finite networks of $N$ excitable quadratic integrate-and-fire neurons, connected via synapses modeled as pulses of finite amplitude and duration. For such synapses, by introducing two distinct types of synaptic events (pulse emission and termination), we were able to write down an exact event-driven map for the system and to evaluate the splay state solutions. For $M$ overlapping postsynaptic potentials, the linear… 
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References

SHOWING 1-10 OF 43 REFERENCES
Stability of the splay state in pulse-coupled networks.
TLDR
It is found that the splay state can be stable even for inhibitory coupling, and the spectrum of Floquet exponents turns out to consist of a number of "isolated" eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities.
Asynchronous States and the Emergence of Synchrony in Large Networks of Interacting Excitatory and Inhibitory Neurons
TLDR
This work investigates theoretically the conditions for the emergence of synchronous activity in large networks, consisting of two populations of extensively connected neurons, one excitatory and one inhibitory, and shows that these mechanisms can be differentiated by the firing patterns they generate and their dependence on the mutual interactions of the inhibitory neurons and cross talk between the two populations.
Stability of splay states in globally coupled rotators.
TLDR
The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of N globally pulse-coupled rotators (neurons) subject to a generic velocity field and it is found that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field.
A Dynamical Theory of Spike Train Transitions in Networks of Integrate-and-Fire Oscillators
TLDR
It is shown how strong coupling instabilities can induce transitions to nonphase locked states characterized by periodic or quasi-periodic variations of the interspike intervals on attracting invariant circles.
Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses.
  • P. Bressloff
  • Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
TLDR
Extensions of the mean-field results to finite networks are developed in terms of the nonlinear firing time map and how stability depends on the degree of synaptic depression or facilitation.
Gamma Oscillation by Synaptic Inhibition in a Hippocampal Interneuronal Network Model
TLDR
It is demonstrated that large-scale network synchronization requires a critical (minimal) average number of synaptic contacts per cell, which is not sensitive to the network size, and that the GABAA synaptic transmission provides a suitable mechanism for synchronized gamma oscillations in a sparsely connected network of fast-spiking interneurons.
Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons
  • N. Brunel
  • Biology
    Journal of Computational Neuroscience
  • 2004
The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous
Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models
TLDR
This work focuses on planar piecewise linear models that can mimic the firing response of several different cell types, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level.
Desynchronization in diluted neural networks.
TLDR
The dynamical behavior of a weakly diluted fully inhibitory network of pulse-coupled spiking neurons is investigated, and the paradox is solved by drawing an analogy with the phenomenon of "stable chaos" by observing that the stochasticlike behavior is "limited" to an exponentially long transient.
Stationary Bumps in Networks of Spiking Neurons
TLDR
It is shown that a bump solution can exist in a spiking network provided the neurons fire asynchronously within the bump, and that the activity profile matches that of a corresponding population rate model.
...
...