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Related papers: Pulse bifurcations in stochastic neural fields

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We consider pulse-coupled Leaky Integrate-and-Fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the…

Chaotic Dynamics · Physics 2015-04-14 D. Angulo-Garcia , A. Torcini

Traveling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrodinger…

Analysis of PDEs · Mathematics 2024-03-07 Tomas Dohnal , Dmitry E. Pelinovsky , Guido Schneider

A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…

Analysis of PDEs · Mathematics 2023-07-18 José Antonio Carrillo , Pierre Roux , Susanne Solem

Persistent neural activity underlying working memory requires sustained synaptic transmission, yet the metabolic and neurotransmitter support provided by astrocyte networks is largely absent from spatially extended neural circuit models. We…

Neurons and Cognition · Quantitative Biology 2026-04-14 Noah Palmer , Heather L. Cihak , Daniele Avitabile , Zachary P. Kilpatrick

We study localized patterns in an exact mean-field description of a spatially-extended network of quadratic integrate-and-fire (QIF) neurons. We investigate conditions for the existence and stability of localized solutions, so-called bumps,…

Pattern Formation and Solitons · Physics 2020-04-22 Helmut Schmidt , Daniele Avitabile

Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…

chao-dyn · Physics 2015-06-24 Manojit Roy , R. E. Amritkar

Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under…

Probability · Mathematics 2020-01-16 Eva Lang , Wilhelm Stannat

We find that sensory noise delivered together with a weak periodic signal not only enhances nonlinear response of neuronal networks, but also improves the synchronization of the response to the signal. We reveal this phenomenon in neuronal…

Neurons and Cognition · Quantitative Biology 2015-08-25 M. A. Lopes , K. -E. Lee , A. V. Goltsev , J. F. F. Mendes

We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…

Probability · Mathematics 2026-01-07 Chang Liu , Dejun Luo

Quantum walks represent an excellent testbed for investigating the interplay between unitary coherent and incoherent dissipative processes. Thanks to photonic quantum interferometers of considerable size, experimental studies could be…

Inspired by applications, we consider reaction-diffusion equations on $\mathbb{R}$ that are stochastically forced by a small multiplicative noise term that is white in time, coloured in space and invariant under translations. We show how…

Analysis of PDEs · Mathematics 2020-03-09 Christian Hamster , Hermen Jan Hupkes

Using an exactly solvable cortical model of a neuronal network, we show that, by increasing the intensity of shot noise (flow of random spikes bombarding neurons), the network undergoes first- and second-order non-equilibrium phase…

Biological Physics · Physics 2015-08-26 K. -E. Lee , M. A. Lopes , A. V. Goltsev

We study the overdamped motion of a particle in a bistable potential subject to the action of a bichromatic force and additive noise, within the context of the vibrational resonance phenomenon. Under appropriate conditions, we obtain…

Statistical Mechanics · Physics 2016-08-16 Jesús Casado-Pascual , José Pablo Baltanás

A common model to study pattern formation in large groups of neurons is the neural field. We investigate a neural field with excitatory and inhibitory neurons, like Wilson and Cowan (1972), with transmission delays and gap junctions. We…

Dynamical Systems · Mathematics 2023-02-20 Len Spek , Stephan A. van Gils , Yuri A. Kuznetsov , Mónika Polner

We consider the existence of standing pulse solutions of a neural network integro-differential equation. These pulses are bistable with the zero state and may be an analogue for short term memory in the brain. The network consists of a…

Neurons and Cognition · Quantitative Biology 2009-11-10 Yixin Guo , Carson C. Chow

We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a non-saturating nonlinear…

Neurons and Cognition · Quantitative Biology 2007-05-23 Yixin Guo , Carson C. Chow

A single qubit driven by an appropriate sequence of control pulses can serve as a spectrometer of local noise affecting its energy splitting. We show that by driving and observing two spatially separated qubits, it is possible to…

Mesoscale and Nanoscale Physics · Physics 2016-07-27 Piotr Szańkowski , Marek Trippenbach , Łukasz Cywiński

In this work we study the noise induced effects on the dynamics of short polymers crossing a potential barrier, in the presence of a metastable state. An improved version of the Rouse model for a flexible polymer has been adopted to mimic…

Statistical Mechanics · Physics 2009-11-13 N. Pizzolato , A. Fiasconaro , B. Spagnolo

This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…

Dynamical Systems · Mathematics 2019-10-08 Hongbo Fu , Dirk Blömker

Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective…

Statistical Mechanics · Physics 2009-11-10 Silvia De Monte , Francesco d'Ovidio , Hugues Chaté , Erik Mosekilde