The simplest problem in the collective dynamics of neural networks: is synchrony stable?

M Timme, F Wolf - Nonlinearity, 2008 - iopscience.iop.org
For spiking neural networks we consider the stability problem of global synchrony, arguably
the simplest non-trivial collective dynamics in such networks. We find that even this simplest …

Duration of transient oscillations in ring networks of unidirectionally coupled neurons

Y Horikawa, H Kitajima - Physica D: Nonlinear Phenomena, 2009 - Elsevier
Properties of the duration of long lasting transient oscillations in ring networks of
unidirectionally coupled sigmoidal neurons are derived with a kinematical model of traveling …

Exponential transient propagating oscillations in a ring of spiking neurons with unidirectional slow inhibitory synaptic coupling

Y Horikawa - Journal of Theoretical Biology, 2011 - Elsevier
Transient oscillations in a ring of spiking neuron models unidirectionally coupled with slow
inhibitory synapses are studied. There are stable spatially fixed steady firing–resting states …

Bifurcation and stabilization of oscillations in ring neural networks with inertia

YO Horikawa, H Kitajima - Physica D: Nonlinear Phenomena, 2009 - Elsevier
Effects of inertia on oscillations in ring networks of unidirectionally coupled sigmoidal
neurons are studied. It is known that ring neural networks without inertia are bistable and the …

Transient chaotic rotating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol oscillators near a codimension-two bifurcation point

Y Horikawa, H Kitajima - Chaos: An Interdisciplinary Journal of …, 2012 - pubs.aip.org
Propagating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol
(BVP) oscillators were studied. The parameter values of the BVP oscillators were near a …

Effects of noise and variations on the duration of transient oscillations in unidirectionally coupled bistable ring networks

Y Horikawa, H Kitajima - Physical Review E—Statistical, Nonlinear, and Soft …, 2009 - APS
We study effects of spatiotemporal noise and spatial variations on long-lasting transient
oscillations in ring networks of unidirectionally coupled bistable elements (neurons), the …

Exponential transient rotating waves in a bistable ring of unidirectionally coupled maps

Y Horikawa, H Kitajima - Physica D: Nonlinear Phenomena, 2012 - Elsevier
Properties of transient rotating waves in a bistable ring of unidirectionally coupled
antisymmetric cubic maps are studied. A kinematical model shows that the duration of …

Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons

Y Horikawa - Neural networks, 2014 - Elsevier
Transient rotating waves in a ring of sigmoidal neurons with asymmetric bidirectional
coupling and self-coupling were studied. When a pair of stable steady states and an …

Duration of transient fronts in a bistable reaction-diffusion equation in a one-dimensional bounded domain

Y Horikawa - Physical Review E—Statistical, Nonlinear, and Soft …, 2008 - APS
The duration of transient fronts in a bistable reaction-diffusion equation in a bounded
domain is considered. The speed of the front decreases exponentially with the length of the …

On the stationary state of a network of inhibitory spiking neurons

W Kinzel - Journal of Computational Neuroscience, 2008 - Springer
The background activity of a cortical neural network is modeled by a homogeneous integrate-
and-fire network with unreliable inhibitory synapses. For the case of fast synapses …