Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses
From MaRDI portal
Publication:2783707
DOI10.1137/S0036139900346453zbMath1001.92021MaRDI QIDQ2783707
David J. Pinto, G. Bard Ermentrout
Publication date: 17 April 2002
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Related Items (only showing first 100 items - show all)
Caristi-type conditions in constraint minimisation of mappings in metric and partially ordered spaces ⋮ Phase Reduction of Waves, Patterns, and Oscillations Subject to Spatially Extended Noise ⋮ Multiscale Motion and Deformation of Bumps in Stochastic Neural Fields with Dynamic Connectivity ⋮ Absolute stability and synchronization in neural field models with transmission delays ⋮ Velocity Integration in a Multilayer Neural Field Model of Spatial Working Memory ⋮ Neural field models with threshold noise ⋮ Exponential dichotomies for nonlocal differential operators with infinite range interactions ⋮ Random attractors for stochastic discrete complex Ginzburg–Landau equations with long-range interactions ⋮ Modeling focal epileptic activity in the Wilson-cowan model with depolarization block ⋮ Wave fronts in inhomogeneous neural field models ⋮ Error analysis of a specialized numerical method for mathematical models from neuroscience ⋮ Exact Neural Fields Incorporating Gap Junctions ⋮ Slow waves in mutually inhibitory neuronal networks ⋮ Bifurcations of lurching waves in a thalamic neuronal network ⋮ Waves, bumps, and patterns in neural field theories ⋮ Continuous neural network with windowed Hebbian learning ⋮ Ghosts of bump attractors in stochastic neural fields: bottlenecks and extinction ⋮ Existence and nonexistence of traveling pulses in a lateral inhibition neural network ⋮ Dynamical Consequences of Fast-Rising, Slow-Decaying Synapses in Neuronal Networks ⋮ SPATIAL HAMILTONIAN IDENTITIES FOR NONLOCALLY COUPLED SYSTEMS ⋮ Dynamic instabilities in scalar neural field equations with space-dependent delays ⋮ Dynamical Synapses Enhance Neural Information Processing: Gracefulness, Accuracy, and Mobility ⋮ Neural Information Processing with Feedback Modulations ⋮ Periodic traveling waves in SIRS endemic models ⋮ Spatiotemporal pattern formation in two-dimensional neural circuits: roles of refractoriness and noise ⋮ Turing instability and pattern formation in a two-population neuronal network model ⋮ Traveling waves in non-local pulse-coupled networks ⋮ Scalar Reduction of a Neural Field Model with Spike Frequency Adaptation ⋮ A simple mathematical model inspired by the Purkinje cells: from delayed travelling waves to fractional diffusion ⋮ Bifurcations and Dynamics in Modified Two Population Neuronal Network Models ⋮ Target patterns in a 2D array of oscillators with nonlocal coupling ⋮ Wave speed analysis of traveling wave fronts in delayed synaptically coupled neuronal networks ⋮ Cortical stimulation in aphasia following ischemic stroke: toward model-guided electrical neuromodulation ⋮ Robust stabilization of delayed neural fields with partial measurement and actuation ⋮ Existence and uniqueness of wave fronts in neuronal network with nonlocal post-synaptic axonal and delayed nonlocal feedback connections ⋮ An integro-differential equation model for the spread of alcohol abuse ⋮ Traveling Pulses in a Nonlocal Equation Arising Near a Saddle-Node Infinite Cycle Bifurcation ⋮ On the spectra of certain integro-differential-delay problems with applications in neurodynamics ⋮ Rotating spirals in oscillatory media with nonlocal interactions and their normal form ⋮ Analysis of a hyperbolic geometric model for visual texture perception ⋮ How effective delays shape oscillatory dynamics in neuronal networks ⋮ Influence of neural adaptation on dynamics and equilibrium state of neural activities in a ring neural network ⋮ Travelling waves in arrays of delay-coupled phase oscillators ⋮ Encoding certainty in bump attractors ⋮ Large fronts in nonlocally coupled systems using Conley-Floer homology ⋮ The weakly nonlocal limit of a one-population Wilson-Cowan model ⋮ Nonlinear analysis of periodic waves in a neural field model ⋮ Numerical bifurcation theory for high-dimensional neural models ⋮ The link between integral equations and higher order ODEs. ⋮ Travelling waves in a neural field model with refractoriness ⋮ Existence of wave front solutions of an integral differential equation in nonlinear nonlocal neuronal network ⋮ Stability of bumps in a two-population neural-field model with quasi-power temporal kernels ⋮ Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations ⋮ Existence of pulses in excitable media with nonlocal coupling ⋮ ISS-Stabilization of Delayed Neural Fields by Small-Gain Arguments ⋮ The effects of noise on binocular rivalry waves: a stochastic neural field model ⋮ Moving bumps in theta neuron networks ⋮ Traveling Bumps and Their Collisions in a Two-Dimensional Neural Field ⋮ The group-theoretical analysis of nonlocal Benney equation ⋮ Neural Fields with Rebound Currents: Novel Routes to Patterning ⋮ From invasion to extinction in heterogeneous neural fields ⋮ Interface dynamics in planar neural field models ⋮ Distributed nonlocal feedback delays May destabilize fronts in neural fields, distributed transmission delays do not ⋮ Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network ⋮ An application of symmetry groups to nonlocal continuum mechanics ⋮ Speeds of traveling waves in some integro-differential equations arising from neuronal networks ⋮ Dynamics of neuronal waves ⋮ Identification of a free energy functional in an integro-differential equation model for neuronal network activity. ⋮ Exponential stability of traveling pulse solutions of a singularly perturbed system of integral differential equations arising from excitatory neuronal networks ⋮ Local excitation-lateral inhibition interaction yields oscillatory instabilities in nonlocally interacting systems involving finite propagation delay ⋮ Analysis of nonlocal neural fields for both general and gamma-distributed connectivities ⋮ Influence of sodium currents on speeds of traveling wave fronts in synaptically coupled neuronal networks ⋮ Stability of bumps in piecewise smooth neural fields with nonlinear adaptation ⋮ The mechanisms for compression and reflection of cortical waves ⋮ Persistence of spatial patterns produced by neural field equations ⋮ Threshold of Front Propagation in Neural Fields: An Interface Dynamics Approach ⋮ A General Framework for Stochastic Traveling Waves and Patterns, with Application to Neural Field Equations ⋮ Regularization of ill-posed point neuron models ⋮ The dynamics of neural fields on bounded domains: an interface approach for Dirichlet boundary conditions ⋮ A rate-reduced neuron model for complex spiking behavior ⋮ Wave Phenomena in Neuronal Networks ⋮ The evolution of synaptically generated waves in one- and two-dimensional domains ⋮ Stabilization of pulse waves through inhibition in a feedforward neural network ⋮ Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions ⋮ Entrainment in up and down states of neural populations: non-smooth and stochastic models ⋮ Persistent Neural States: Stationary Localized Activity Patterns in Nonlinear Continuous n-Population, q-Dimensional Neural Networks ⋮ Asymptotic behavior for a non-autonomous model of neural fields with variable external stimulus ⋮ Two-point heterogeneous connections in a continuum neural field model ⋮ Travelling corners for spatially discrete reaction-diffusion systems ⋮ DYNAMICS OF DELAY-COUPLED EXCITABLE NEURAL SYSTEMS ⋮ Existence and Uniqueness of Traveling Fronts in Lateral Inhibition Neural Fields with Sigmoidal Firing Rates ⋮ Traveling Waves for Spatially Discrete Systems of FitzHugh--Nagumo Type with Periodic Coefficients ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On inclusions arising in neural field modeling ⋮ Tutorial on Neural Field Theory ⋮ Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation ⋮ PDE Methods for Two-Dimensional Neural Fields ⋮ Heterogeneous Connectivity in Neural Fields: A Stochastic Approach ⋮ Traveling waves of a singularly perturbed system of integral-differential equations arising from neuronal networks
This page was built for publication: Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses