Verhulst and bifurcation analyses of a neuronal network on an outer-totalistic toroidal cellular automata

Abstract

Our cellular automata (CA) model of a neuronal patch is a fast way of exploring the dynamics of population of interconnected neurons. In this study, we analyzed the cobweb diagrams of our model and found that the nonzero steady-state neuronal activity is an emergent property of our model. We investigated if there exists a bifurcation and found that the period-doubling happens at negatively-sloped activation function. Neurons exhibiting this characteristic implies a possible way of modelling epileptic neurons. We propose the categorization of neuronal CA as follows: Class 0 (Zero steady-state), Class 1 (Nonzero steady-state), and Class 2 (Periodic steady-state).