Steady-state spiking behaviors of neuronal patch model based on an extension of Brian's brain cellular automata

Abstract

The Brian’s brain cellular automata is a simplistic model that captures the basic dynamics of a neuronal patch based on the structure of game of life. In this work, we extend the model to more realistically capture the neuronal spiking process given a stimulus Λ and firing threshold λ. We characterize the spatiotemporal dynamics by varying the threshold value λ. Four steady-state behaviors are observed for the case Λ = λ: Class 0 (inactive), Class 1a (spiking with local blinker), Class 1b (spiking with gliders), and Class 2 (oscillatory or global blinker with period-4). For the modified transition rule Λ ≥ λ, the resulting dynamics are interactions of the basic Brian's brain rules producing unique patterns with properties remnant to each rule. Whether these interactions are linear or nonlinear superposition was not explored in this work. In summary, oscillating neuronal patch activity is observed when the firing threshold is low, while higher firing threshold allows the neuron to converge into a more stable activity. The steady-state behaviors for the modified Brian's brain are as follows: Class 0 (inactive), Class 1 (spiking with gliders and glider guns), and Class 2 (oscillatory or global blinker with period-3). The classification corresponds to different types of biological neurons, e.g. oscillatory mimics epileptic neurons during seizure.