Modeling of neural systems by use of neuronal modes

A methodology for modeling spike-output neural systems from input-output data is proposed, which makes use of "neuronal modes" (NM) and "multi-input threshold" (MT) operators. The modeling concept of NMs was introduced in a previously published paper (V.Z. Marmarelis, ibid., vol.36, p.15-24, 1989) in order to provide concise and general mathematical representations of the nonlinear dynamics involved in signal transformation and coding by a class of neural systems. The authors present and demonstrate (with computer simulations) a method by which the NMs are determined using the 1stand 2nd-order kernel estimates of the system, obtained from input-output data. The MT operator (i.e., a binary operator with multiple real-valued operands which are the outputs of the NMs) possesses an intrinsic refractory mechanism and generates the sequence of output spikes. The spike-generating characteristics of the MT operator are determined by the "trigger regions" defined on the basis of data. This approach is offered as a reasonable compromise between modeling complexity and prediction accuracy, which may provide a common methodological framework for modeling a certain class of neural systems.