The simplest problem in the collective dynamics of neural networks: is synchrony stable?
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 …
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 …
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 …
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 …
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 …
(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 …
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 …
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 …
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 …
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 …
and-fire network with unreliable inhibitory synapses. For the case of fast synapses …