TY  - JOUR
A1  - Goychuk, Igor
A1  - Goychuk, Andriy
T1  - Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay
JF  - New journal of physics : the open-access journal for physics
N2  - We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around -1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence.
KW  - neuronal networks
KW  - stochastic models
KW  - memory and delay
KW  - critical avalanche dynamics
Y1  - 2015
U6  - https://doi.org/10.1088/1367-2630/17/4/045029
SN  - 1367-2630
VL  - 17
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Goychuk, Igor
A1  - Goychuk, Andriy
T1  - Stochastic Wilson
BT  - Cowan models of neuronal network dynamics with memory and delay
JF  - New journal of physics
N2  - We consider a simple Markovian class of the stochastic Wilson–Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around −1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence.
KW  - neuronal networks
KW  - stochastic models
KW  - memory and delay
KW  - critical avalanche dynamics
Y1  - 2015
U6  - https://doi.org/10.1088/1367-2630/17/4/045029
SN  - 1367-2630
VL  - 17
IS  - 4
PB  - Deutsche Physikalische Gesellschaft, Institute of Physics
CY  - Bad Honnef, London
ER  -