An analysis of recurrent excitation based on non-linear discrete dynamical system theory and its relevance to epileptogenesis.

*(English)*Zbl 1061.92022Summary: Recurrent Excitation (RE) is known to occur in neurons of the hippocampal formation and is considered to be an important mechanism mediating memory and epileptogenesis. We analyzed this RE neural network using discrete dynamical system theory, and establish an equation to assess the intrinsic properties of this circuitry. Our analysis revealed that at equilibrium the number of neurons firing in synchrony is a function of the ratio between inhibition and excitation. Additionally, the analysis showed that the RE network is intrinsically hyperexcitable. Depending on the level of inhibition or excitation, the system existed in one of five states. There were four stable non-oscillatory states, and one stable oscillatory two-cycle state. Further analysis of these states indicated that the best maneuver to control the number of neurons firing synchronously is not uniform, and is dependent on the initial conditions of the system. Thus, increasing the amount of inhibition facilitated hypersynchrony if the system was in a stable oscillatory two cycle state. In this two-cycle state, a reduction in level of excitation facilitated a reduction in the number of neurons firing synchronously.

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\textit{R. Manon-Espaillat} and \textit{M. Eisen}, Int. J. Nonlinear Sci. Numer. Simul. 2, No. 4, 321--327 (2001; Zbl 1061.92022)

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