Firing patterns transition and network dynamics of an extended Hindmarsh-Rose neuronal system.

Analysis of Hindmarsh-Rose (HR) neural model and its network dynamics under different inputs or network topologies are the leading research of the structural dynamics of complex networks, but the typical three-variable HR neural model has limitations in describing the complex non-linear features and precise behavior patterns of neuron. Based on an extended HR neural model, the firing patterns and bifurcation behavior are analysed in this paper, and how the newly introduced variable affect discharge modes has also been explored. A two-dimensional lattice is constructed to study the mechanism of spiral wave formation and breakup in the neural network, and to explore its network dynamics and synchronous behavior. Obtained results show that the extended HR neural model has more rich and stable firing properties, and it can be observed that there are multimodal phenomena with both spiking and bursting states simultaneously. If the network topology is changed, the formation and breakup of spiral waves can be observed, and the synchronization factor exhibits a monotonically decreasing relationship with the coupling strength and the control parameters of the newly introduced variable. When HR neurons are in spiking state, the system is more prone to spiral waves, and the coupling strength range for spiral waves is wider. The above results provide valuable ideas to explore the modulation of network group behavior. [ABSTRACT FROM AUTHOR]