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Essential tutorial on myelin, oligodendrocytes and their functional relevance in the pathophysiology of the brain., Comment: 14 pages. Submitted as contributed section to the chapter on "Neurophysiology" of the book "Da\~no cerebral" (Brain damage), JC Arango-Asprilla \& L Olabarrieta-Landa eds. Manual Moderno Editions

We use tools of bifurcation theory to characterize dynamics of astrocytic~IP$_3$ and~Ca$^{2+}$ for different~IP$_3$ regimes from a mathematical point of view. We do so following a bottom-up approach, starting from a compact, well-stirred astrocyte model to first identify characteristic~IP$_3$ pathways whereby~Ca$^{2+}$ (and~IP$_3$) dynamics "bifurcate", namely change from stable (constant) concentration levels, to oscillatory dynamics. Then we extend our analysis to the elemental case of two astrocytes, coupled by~IP$_3$ diffusion mediated by gap junction channels, putting emphasis on the mechanisms of emergence of chaotic oscillations. Finally, we complete our analysis discussing spatiotemporal~Ca$^{2+}$ dynamics in a spatially-extended astrocyte model, gaining insights on the possible physical mechanisms whereby random Ca$^{2+}$~generation could be orchestrated into robust, spatially-confined intracellular~Ca$^{2+}$ oscillations., Comment: 19 pages (24 pages with References), 1 table, 5 figures, book chapter