Approximate-master-equation approach for the Kinouchi-Copelli neural model on networks

Abstract

In this work, we use the approximate-master-equation approach to study the dynamics of the Kinouchi-Copelli neural model on various networks. By categorizing each neuron in terms of its state and also the states of its neighbors, we are able to uncover how the coupled system evolves with respective to time by directly solving a set of ordinary differential equations. In particular, we can easily calculate the statistical properties of the time evolution of the network instantaneous response, the network response curve, the dynamic range, and the critical point in the framework of the approximate-master-equation approach. The possible usage of the proposed theoretical approach to other spreading phenomena is briefly discussed.

Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems

“…Concerning the simulations, we must make a technical observation. In contrast to the static model 24 , the relevant indicator of criticality here is no longer the branching ratio σ , but the principal eigenvalue Λ ≠ σ of the synaptic matrix P ij , with Λ c = 1 48,51 . This occurs because the synaptic dynamics creates correlations in the random neighbour network 26 .…”

Mechanisms of Self-Organized Quasicriticality in Neuronal Network Models

“…[7,[21][22][23][24][25][26][27]). One of the main results is that information processing seems to be optimized at a secondorder absorbing phase transition [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. This transition occurs between no activity (the absorbing phase) and nonzero steadystate activity (the active phase).…”

Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding

“…For concreteness we employ a general model of excitable networks [17,27,28], adapted to incorporate nodal heterogeneity [29]. Susceptible (quiescent) nodes can be excited either by (global) external driving or by (local) neighbour contributions: External inputs arrive at a steady Poisson rate h. An input rate h indicates that at each time step δt (=1 ms), an external input may arrive with a probability p h = 1 − exp(−hδt).…”

“…For concreteness we employ a general model of excitable networks [20,30,31], adapted to incorporate nodal heterogeneity [32]. Susceptible (quiescent) nodes can be excited either by (global) external driving or by (local) neighbour contributions.…”