Impact of distance-dependent power-law coupling on chimera states in FitzHugh–Nagumo neuronal networks

This paper investigates the collective dynamics and transition mechanisms in a network of FitzHugh–Nagumo oscillators coupled via a distance-dependent power-law scheme. Varying the power-law exponent, which governs the spatial decay of coupling strength, drives the network from global to local connectivity, leading to distinct transitions in spatiotemporal behavior. To quantitatively characterize these transitions, we employ several measures, including the Kuramoto order parameter, the strength of incoherence, and the similarity function. Our results reveal that the interplay between coupling topology and strength gives rise to a rich repertoire of dynamical states, such as chimera states, cluster synchronization, and lag synchronization. Remarkably, lag-synchronized clusters emerge robustly in regimes of highly localized coupling, even under weak interactions. Furthermore, we compare globally and nonlocally coupled networks and show that the coupling range critically influences the onset and structure of these patterns.