Related papers: Excitable elements controlled by noise and network…
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…
We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
Many natural systems including the brain comprise coupled non-uniformly stimulated elements. In this paper we show that heterogeneously driven networks of excitatory-inhibitory units exhibit striking collective phenomena, including…
We consider a model of large regulatory gene expression networks where the thresholds activating the sigmoidal interactions between genes and the signs of these interactions are shuffled randomly. Such an approach allows for a qualitative…
Critical phenomena in globally coupled excitable elements are studied by focusing on a saddle-node bifurcation at the collective level. Critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We study complex networks of stochastic two-state units. Our aim is to model discrete stochastic excitable dynamics with a rest and an excited state. Both states are assumed to possess different waiting time distributions. The rest state is…
We study the emergence and coherence of stochastic oscillations in star networks of excitable elements in which peripheral nodes receive independent random inputs. A biophysical model of a distal branch of sensory neuron in which peripheral…
According to the chemical reaction network theory, the topology of a certain class of chemical reaction networks, regardless of the kinetic details, sets a limit on the dynamical properties that a particular network can potentially admit;…
The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…
We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to…
Various functions of a network of excitable units can be enhanced if the network is in the `critical regime', where excitations are, on average, neither damped nor amplified. An important question is how can such networks self-organize to…
This paper develops a mathematical framework to study signal networks, in which nodes can be active or inactive, and their activation or deactivation is driven by external signals and the states of the nodes to which they are connected via…
We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase…