Related papers: Can dynamical synapses produce true self-organized…
We investigate the dynamics of two models of biological networks with purely suppressive interactions between the units; species interacting via niche competition and neurons via inhibitory synaptic coupling. In both of these cases,…
We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed…
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
A multispecies artificial ecosystem is formulated using cellular automata with species interactions and food chain hierarchy. The constructed finite state automaton can simulate the complexity and self-organized characteristics of the…
Signatures of self-organized criticality (SOC) have recently been observed in an ultracold atomic gas under continuous laser excitation to strongly-interacting Rydberg states [S. Helmrich et al., Nature, 577, 481--486 (2020)]. This creates…
The spontaneous emergence of scale invariance, called self-organized criticality (SOC), is often attributed to a second-order absorbing-state phase transition (ASPT). Many real-world systems display SOC, yet extreme events are often…
A system is in a self-organized critical state if the distribution of some measured events (avalanche sizes, for instance) obeys a power law for as many decades as it is possible to calculate or measure. The finite-size scaling of this…
We investigate states of enhanced activity in a biological neuronal network composed of pulse-coupled oscillators. The synaptic couplings between the neurons are dynamic, modeling spike time dependent plasticity. The network exhibits…
Directed complex network of two-state model neurons linked by synapses which can be blocked or activated stochastically in time undergoes phase transition between the quiescent phase with zero activity and the active one with persistent…
Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $\nu(t)$ scale with the…
Statistical features of "bursty" behaviour in charged and neutral fluid turbulence, are compared to statistics of intermittent events in a GOY shell model, and avalanches in different models of Self Organized Criticality (SOC). It is found…
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…
Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness…
The original sandpile model of Bak, Tang and Wiesenfeld from 1987 has inspired lots of consequent work and further ideas of how to describe the birth of scale-invariant statistics in various systems and in particular models. In this article…
The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory--inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in…
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one…
We investigate a one-dimensional three-species dynamical model whose dynamics naturally generate the semi-directed percolation cluster in time and show a non-equilibrium absorbing state phase transition from an active to inactive state. The…
A stochastic cellular automaton exhibiting parity conserving class transition has been investigated in the presence of quenched spatial disorder by large scale simulations. Numerical evidence has been found that weak disorder causes…