title: Traveling bumps and their collisions in a two-dimensional neural field.
abstract: A neural field is a continuous version of a neural network model accounting for dynamical pattern forming from populational firing activities in neural tissues. These patterns include standing bumps, moving bumps, traveling waves, target waves, breathers, and spiral waves, many of them observed in various brain areas. They can be categorized into two types: a wave-like activity spreading over the field and a particle-like localized activity. We show through numerical experiments that localized traveling excitation patterns (traveling bumps), which behave like particles, exist in a two-dimensional neural field with excitation and inhibition mechanisms. The traveling bumps do not require any geometric restriction (boundary) to prevent them from propagating away, a fact that might shed light on how neurons in the brain are functionally organized. Collisions of traveling bumps exhibit rich phenomena; they might reveal the manner of information processing in the cortex and be useful in various applications. The trajectories of traveling bumps can be controlled by external inputs.
authors.affiliation: Zhongnan University of Economics and Law, Wuhan City, Hubei Province, China. yaoli@mail.znufe.edu.cn
authors.forename: Yao
authors.initials: Y
authors.lastname: Lu
authors.forename: Yuzuru
authors.initials: Y
authors.lastname: Sato
authors.forename: Shun-Ichi
authors.initials: S
authors.lastname: Amari
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000222:Adaptation, Physiological / Q000502:physiology; D000465:Algorithms; D058256:Brain Waves / Q000502:physiology; D002540:Cerebral Cortex / Q000502:physiology*; D003198:Computer Simulation / Q000592:standards; D004574:Electromagnetic Fields; D019706:Excitatory Postsynaptic Potentials / Q000502:physiology; D006801:Humans; D053444:Inhibitory Postsynaptic Potentials / Q000502:physiology; D055641:Mathematical Concepts; D008962:Models, Theoretical; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009435:Synaptic Transmission / Q000502:physiology*