Elimination of spiral waves in a two-dimensional Hindmarsh–Rose neural network under long-range interaction effect and frequency excitation

The elimination of spiral waves is numerically studied in a network of Hindmarsh–Rose neurons in presence of long-range diffusive interactions and external frequency excitations. Some features of membrane potential, including time series, spatiotemporal and spatial diagrams are discussed. It is found that at low frequency excitations, weak and strong long-range couplings sustain target wave propagation and spiral wave formation. However, ultra-long-range connections fully suppress such patterns, especially in the case of a Kac–Baker-like long-range coupling. In addition, increase in the excitation frequency supports the transition from stable robust spiral waves to spiral turbulence at weak or strong long-range connections. The interplay between hyper-high-frequency excitation and Kac–Baker-like long-range interaction completely eliminates spiral waves and only regenerates target wave propagation. Our results suggest that both frequency excitation regimes and long-range interaction may efficiently regulate the electrical activity of thalamus neurons and effectively prevent some brain disorders such as epileptic seizures. •A network of Hindmarsh–Rose neurons is used to numerically study the elimination of spiral waves in presence of long-range interactions and external frequency excitations.•Low frequency excitations, weak and strong long-range couplings sustain target waves propagation and spiral waves formation.•Ultra-long-range connections fully suppress such patterns.•High excitation frequency supports transition from stable spiral waves to spiral turbulence for weak/strong long-range connections.