Totalistic cellular automata model of a neuronal network on a spherical surface

Abstract

Our understanding of how the brain works is still an open challenge. Current neuronal models (e.g. integrate-and-fire, Hodgkin-Huxley) are able to mimic voltage patterns in neurons using ordinary differential equations. Coupling these models would be difficult to solve manually and numerically. Previously, we proposed a cellular automata neuronal model that would efficiently simulate the dynamics of a large number of neurons. We chose a linear activation function that mimics the neuronal response of an integrate-and-fire neuron. In this paper, we extended our analysis by comparing nontotalistic vs totalistic modes. We also investigated how a spherical lattice topology affects the neuronal network dynamics as opposed to the previous toroidal topology. Finally, we were able to find three dynamical categories that we previously observed, by considering the length of the activation function and the fraction of initially active neurons.