Spatiotemporal dynamics of a food chain model incorporating higher-order interactions and slow–fast effect

Higher-order interactions (HOIs), as critical drivers of complex dynamical behaviors in ecosystems, have garnered increasing attention in scientific research. Existing studies have demonstrated their significant regulatory effects on multispecies coexistence and biodiversity. However, the mechanisms through which HOIs influence ecosystem spatial dynamics remain poorly understood. This study constructs a time delay reaction–diffusion food chain model with HOIs and slow–fast effect. We established the local asymptotic stability conditions for the positive equilibrium point of system by employing linear stability analysis. Utilizing amplitude equation theory, we reveal the mechanisms underlying Turing instability and the formation patterns of spatial structures. Furthermore, by selecting time delay as a bifurcation parameter, we derive the criteria for Hopf bifurcation. Numerical simulations validate the theoretical predictions and further demonstrate that variations in HOIs intensity and slow–fast effect significantly alter spatial constructures, inducing diverse spiral patterns.