Summary
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.
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The research reported in this paper was supported in part by NIH GM2037
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Ermentrout, G.B., Cowan, J.D. Temporal oscillations in neuronal nets. J. Math. Biology 7, 265–280 (1979). https://doi.org/10.1007/BF00275728
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DOI: https://doi.org/10.1007/BF00275728