Effects of higher-order interactions and electromagnetic induction on synchronization in Hindmarsh–Rose neuronal networks

Synchronization phenomena in neuronal networks have a key role in cognitive functions and neural information processing. This study investigates the synchronization behavior of neuronal networks under the combined influence of electromagnetic induction and higher-order interactions. We construct a simplicial complex that incorporates both first- and second-order couplings, and introduce electromagnetic induction into the Hindmarsh–Rose neuronal model. Using the master stability function method and numerical simulations, we analyze the effects of electromagnetic induction strength and the proportion of higher-order interactions on synchronization stability and energy distribution. The results show that moderate electromagnetic induction helps reduce the synchronization threshold and enhances energy uniformity across the network. In contrast, increasing the proportion of higher-order interactions introduces stronger structural heterogeneity and significantly suppresses the synchronization. Spectral analysis reveals an intrinsic link between declining synchronization stability and structural features. Furthermore, simulations on the real-world Dolphin social network validate the generality of the proposed mechanism. This study highlights the synergistic effects of electromagnetic regulation and higher-order coupling in neuronal dynamical systems and provides theoretical insights into synchronization mechanisms in complex networks.