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Rodrigues, V.F., Kalil, C., de Castro, M.C.S., Silva, D. and Cortez, C.M. (2018) Mathematical-Computational Modeling in Behavior’s Study of Repetitive Discharge Neuronal Circuits. In: Alves Barbosa da Silva, F., Carels, N. and Paes Silva Jr., F., Eds., Theoretical and Applied Aspects of Systems Biology, Springer International Publishing AG, Cham, 243-259.
https://doi.org/10.1007/978-3-319-74974-7_13

has been cited by the following article:

• TITLE: Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit

  AUTHORS: Camila de Andrade Kalil, Maria Clícia Stelling de Castro, Dilson Silva, Célia Martins Cortez

  KEYWORDS: Mathematical-Computational Modelling, Neurophysiological Circuit, Reverberating Circuit, Parallel Circuit

  JOURNAL NAME: Open Journal of Modelling and Simulation, Vol.9 No.2, April 29, 2021

  ABSTRACT: The aim of the present study is to contribute to the knowledge about the functioning of the neuronal circuits. We built a mathematical-computational model using graph theory for a complex neurophysiological circuit consisting of a reverberating neuronal circuit and a parallel neuronal circuit, which could be coupled. Implementing our model in C++ and applying neurophysiological values found in the literature, we studied the discharge pattern of the reverberant circuit and the parallel circuit separately for the same input signal pattern, examining the influence of the refractory period and the synaptic delay on the respective output signal patterns. Then, the same study was performed for the complete circuit, in which the two circuits were coupled, and the parallel circuit could then influence the functioning of the reverberant. The results showed that the refractory period played an important role in forming the pattern of the output spectrum of a reverberating circuit. The inhibitory action of the parallel circuit was able to regulate the reverberation frequency, suggesting that parallel circuits may be involved in the control of reverberation circuits related to motive activities underlying precision tasks and perhaps underlying neural work processes and immediate memories.