相关论文: Stable Irregular Dynamics in Complex Neural Networ…
Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been…
We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
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 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…
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…
The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro.…
Large ensembles of globally coupled chaotic neural networks undergo a transition to complete synchronization for high coupling intensities. The onset of this fully coherent behavior is preceded by a regime where clusters of networks with…
We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (``patterns'') we add a slow coupling dynamics that makes the visited patterns…
The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability…
We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and non-isochronocity of the interactions on the pattern formation. A few additional…
We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit…
We study a dynamical model of interconnected firms which allows for certain market imperfections and frictions, restricted here to be myopic price forecasts and slow adjustment of production. Whereas the standard rational equilibrium is…
Cortical networks can maintain memories for decades despite the short lifetime of synaptic strength. Can a neural network store long-lasting memories in unstable synapses? Here, we study the effects of random noise on the stability of…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We…
We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of…
We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the…