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In this study, the objective is to model a neuronal population using cellular automata (CA) rules that are both simple and realistic. Unlike in previous research, the primary aim is to capture a range of neuronal behaviours with minimal complexity and computational overhead. To achieve this, a two-dimensional lattice of cellular automata was implemented in the C++ programming language, with the lattice and cell structure, cell states, neighbourhood interactions, and governing rules being defined. Various behaviours within the neuronal population were simulated by taking into account the resting state and action potential of each neuron. Four distinct behaviours in the model were unveiled by our observations: fixed point, rhythmic, chaotic, and dual behaviour. Importantly, the outcomes of the neuronal CA were significantly influenced by the neighbourhood configuration of a neuron. In particular, a dual behaviour also referred to as an intrinsic bifurcation, was induced when the number of neighbouring cells for a neuron was reduced. In a broader sense, the maximum and minimum neighbour counts for a cell were found to serve as low-pass and high-pass filters, respectively, for the output signal of the CA model.
Yanboyu Zhang (Thu,) studied this question.