Dynamics of delayed and diffusive FitzHugh–Nagumo network.

Higher-order networks reveal intricate structural connections within neural brain models by exposing relationships between multiple nodes. Within human brain networks, information transmission among neurons invariably incurs a time delay, resulting in abnormal discharge of membrane potential. In this study, we analyze correlation visualizations of the Laplacian matrix derived from both general networks and higher-order networks, highlighting eigenvector distributions. The presence of time delay significantly influences the dynamical behavior of the system. Therefore, we examine the phase diagram, identifying firing patterns such as fast-spiking and mixed-mode oscillations. Ultimately, we demonstrate that both time delay and diffusion can alter the dynamical behavior of the FitzHugh–Nagumo model. Notably, within higher-order networks, the phenomenon of Turing instability becomes more pronounced, offering an analogous framework for studying associated diseases. This instability emerges as neuronal states approach abnormal levels, leading to the onset of related diseases. Numerical simulation and data also verify these results. [ABSTRACT FROM AUTHOR]