Related papers: Threshold of front propagation in neural fields: A…
In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased and weakly coupled by tunneling. We develop…
In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…
For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…
Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to…
Initial fluctuations in hydrodynamic fields such as energy density or flow velocity give access to understanding initial state and equilibration physics as well as thermodynamic and transport properties. We provide evidence that the fluid…
Phase-field models have recently had great success in describing the dynamic morphologies and motility of eukaryotic cells. In this work we investigate the minimal phase-field model introduced in [Berlyand, Potomkin, Rybalko (2017)].…
Kinematic equations for the motion of slowly propagating, weakly curved fronts in bistable media are derived. The equations generalize earlier derivations where algebraic relations between the normal front velocity and its curvature are…
We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of…
Understanding how receptive fields emerge and organize within brain networks and how neural dynamics couple with stimuli space is fundamental to neuroscience. Models often rely on fine-tuning connectivity to match empirical data, which may…
In this paper, we systematically investigate both the synfire propagation and firing rate propagation in feedforward neuronal network coupled in an all-to-all fashion. In contrast to most earlier work, where only reliable synaptic…
Active inference is a normative framework for explaining behaviour under the free energy principle -- a theory of self-organisation originating in neuroscience. It specifies neuronal dynamics for state-estimation in terms of a descent on…
We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) Below…
Motivated by results for the propagation of active-passive interfaces of bacterial Serratia marcescens swarms [Nat. Comm., 9, 5373 (2018)] we use a hydrodynamic multiphase model to investigate the propagation of interfaces of active…
Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…
Equilibrium propagation is a recently introduced method to use and train artificial neural networks in which the network is at the minimum (more generally extremum) of an energy functional. Equilibrium propagation has shown good performance…
The dynamical responses of ferromagnet to the propagating electromagnetic field wave passing through it are modelled and studied here by Monte Carlo simulation in two dimensional Ising ferromagnet. Here, the electromagnetic wave is linearly…