Temporal oscillations in neuronal nets.
A model for the interactions of cortical neurons is derived and analyzed. It is shown that small amplitude spatially inhomogeneous standing oscillations can bifurcate from the rest state. In a periodic domain, traveling wave trains exist. Stability of these patterns is discussed in terms of biological parameters. Homoclinic and heteroclinic orbits are demonstrated for the space-clamped system.
D001921:Brain / Q000502:physiology*; D005583:Fourier Analysis; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D009433:Neural Inhibition; D009474:Neurons / Q000502:physiology*; D009991:Oscillometry; D010507:Periodicity; D009435:Synaptic Transmission