相关论文: Noise-induced memory in extended excitable systems

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…

Inhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the analysis of…

We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is…

Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions…

A social system is considered whose agents choose between several alternatives of possible actions. The system is described by the fractions of agents preferring the corresponding alternatives. The agents interact with each other by…

Cortical sensory neurons are known to be highly variable, in the sense that responses evoked by identical stimuli often change dramatically from trial to trial. The origin of this variability is uncertain, but it is usually interpreted as…

We study the random processes with non-local memory and obtain new solutions of the Mori-Zwanzig equation describing non-markovian systems. We analyze the system dynamics depending on the amplitudes $\nu$ and $\mu_0$ of the local and…

Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously…

Neurons fire irregularly on multiple timescales when stimulated with a periodic pulse train. This raises two questions: Does this irregularity imply significant intrinsic stochasticity? Can existing neuron models be readily extended to…

Recently, the field of hardware neural networks has been actively developing, where neurons and their connections are not simulated on a computer but are implemented at the physical level, transforming the neural network into a tangible…

Noise-induced population bursting has been widely identified to play important roles in the information process. We constructed a mathematical model for a random and sparse neural network where bursting can be induced from the resting state…

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…

Cortical neurons are bistable; as a consequence their local field potentials can fluctuate between quiescent and active states, generating slow 0.5-2 Hz oscillations which are widely known as transitions between Up and Down States. Despite…

We consider a dynamic system that is driven by an intensity-modulated Poisson process with intensity $\Lambda(t)=\lambda(t)+\varepsilon\nu(t)$. We derive an exact relation between the input-output cross-correlation in the spontaneous state…

Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…

A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others.…

The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically…

The network studied here is based on a standard model in physics, but it appears in various applications ranging from spintronics to neuroscience. When the network is forced by an external signal common to all its elements, there are shown…

Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…

Stochastic network-dynamics are typically assumed to be memory-less. Involving prolonged dwells interrupted by instantaneous transitions between nodes such Markov networks stand as a coarse-graining paradigm for chemical reactions, gene…