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We use tools of bifurcation theory to characterize dynamics ofastrocytic~IP$_3$ and~Ca$^{2+}$ for different~IP$_3$ regimes from amathematical point of view. We do so following a bottom-up approach, startingfrom a compact, well-stirred astrocyte model to first identifycharacteristic~IP$_3$ pathways whereby~Ca$^{2+}$ (and~IP$_3$) dynamics"bifurcate", namely change from stable (constant) concentration levels, tooscillatory dynamics. Then we extend our analysis to the elemental case of twoastrocytes, 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$^{2+}$ dynamicsin a spatially-extended astrocyte model, gaining insights on the possiblephysical mechanisms whereby random Ca$^{2+}$~generation could be orchestratedinto robust, spatially-confined intracellular~Ca$^{2+}$ oscillations.

Emergence of regular and complex calcium oscillations by inositol 1,4,5-trisphosphate signaling in astrocytes