Bursting, beating, and chaotic modes in mathematical models of the R15 cell in Aplysia

Abstract

Chaotic regimes have been observed experimentally in neurons as well as in deterministic neuronal models. The bursting R15 cell in the abdominal ganglion of Aplysia has been the subject of extensive mathematical modeling. The model of Plant and Kim is capable of exhibiting both bursting and beating modes of electrical activity. We demonstrate (1) that a chaotic regime exists between the bursting and beating modes of the model, and (2) that the model approaches chaos from both modes by a period doubling cascade. We propose an original model of R15 which differs from previous models in several ways: the inclusion of a calcium ion balance, the underlying assumption that the calcium-dependent inactivation of a calcium current rather than the calcium-dependent activation of a potassium current mediates bursting activity, and the incorporation of experimental data to the extent possible. Preliminary results support the contention that a chaotic regime is intermediate between the beating and bursting modes. (Abstract shortened with permission of author.)