Noise-induced stabilization of bumps in systems with long-range spatial coupling

DOI10.1016/S0167-2789(01)00351-7zbMath0997.92002OpenAlexW2127920751MaRDI QIDQ5950436

André Longtin, Carlo R. Laing

Publication date: 11 December 2001

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(01)00351-7

zbMATH Keywords

pitchfork bifurcationslocalized active neuron regionsspatiotemporal noise

Mathematics Subject Classification ID

Neural biology (92C20) Neural networks for/in biological studies, artificial life and related topics (92B20) Bifurcation theory for ordinary differential equations (34C23) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (10)

Velocity Integration in a Multilayer Neural Field Model of Spatial Working Memory ⋮ Generalized discrete and ultradiscrete Burgers equations derived through the correlated random walk ⋮ Ghosts of bump attractors in stochastic neural fields: bottlenecks and extinction ⋮ Scalar Reduction of a Neural Field Model with Spike Frequency Adaptation ⋮ Coherence and stochastic resonance in a periodic potential driven by multiplicative dichotomous and additive white noise ⋮ Numerical bifurcation theory for high-dimensional neural models ⋮ Additive noise driven phase transitions in a predator-prey system ⋮ Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation ⋮ Nonlinear Langevin Equations for Wandering Patterns in Stochastic Neural Fields ⋮ Stochastic Motion of Bumps in Planar Neural Fields

Cites Work

• Noise-induced transitions. Theory and applications in physics, chemistry, and biology
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Handbook of stochastic methods for physics, chemistry and the natural sciences
• Bifurcations in fluctuating systems: The center-manifold approach
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Noise sustained waves in subexcitable media: From chemical waves to brain waves
• Stationary Bumps in Networks of Spiking Neurons
• On the Propagation of Calcium Waves in an Inhomogeneous Medium
• Stochastic processes driven by dichotomous Markov noise: Some exact dynamical results
• Collision of Travelling Waves in a Reaction-Diffusion System with Global Coupling Effect
• The post-processed Galerkin method applied to non-linear shell vibrations
• Instabilities and splitting of pulses in coupled Ginzburg-Landau equations
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