Abstract
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.
Highlights
Network complexity pervades biology and medicine [1], and the human organism can be considered as an integrated complex network of different physiological systems [2] such as circulatory and respiratory systems, visual system, digestive and endocrine systems, etc, which are coordinated by autonomic and central nervous systems including the brain
The difference is barely detectable in figures 3(a), (b), where we present the results of stochastic simulations done both with the exact Gillespie algorithm and within the approximate Langevin dynamics
We compare in figures 3(a), (b), the results for the considered dynamics and its two-variable Markovian approximation given by the standard Wilson–Cowan model in which, the transfer functions are renormalized in accordance with equation (5), where the parameter βτd is replaced by βe γe = 0.1 and βi γi = 0.2, correspondingly
Summary
From the point of view of the dynamics of the individual elements, we are dealing with a attribution to the network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally author(s) and the title of the work, journal citation in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional and DOI. 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.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
