Synchronization and firing patterns of coupled one-dimensional neuron maps

Exploring the collective behavior of neurons in complex networks has been a hot topic in complex network analysis. In this regard, many studies have been conducted to explore the collective behavior of neurons using different flow-based and map-based neuronal models. The map-based models have some advantages over the flow-based models, such as their simplicity, efficiency, and flexibility. This paper investigates the collective behaviors of a recently proposed one-dimensional piecewise nonlinear map-based neuronal model with rich dynamical properties. The neurons are configured in a Watts–Strogatz small-world network structure under five conditions considering electrical synapses, inner linking functions, chemical synapses, both electrical and chemical synapses, and both inner linking and chemical synaptic functions as the neurons’ communication channels. We found that the electrically coupled neurons cannot achieve an entirely synchronous firing pattern; however, in other fourth cases, they can reach a synchronous state. Besides the synchronization state, cluster synchronization, imperfect synchronization, chimera, and solitary state are other firing patterns observed in the studied network.