Pattern Dynamics of a Predator–Prey Model Driven by Higher-Order Interactions

We have developed a predator–prey model driven by higher-order interactions to investigate their potential in stabilizing ecological community dynamics and promoting species coexistence. Initially, the stability of the equilibrium is analyzed under diffusion-free conditions, and its local bifurcation behavior is systematically examined. In alignment with real ecological scenarios, higher-order interactions are modeled as random simplicial complexes. Moreover, a network dynamics approach is employed to study the pattern dynamics induced by higher-order interactions. Perturbation analysis is conducted to identify parametric conditions that lead to Turing instability. The results indicate that higher-order interactions play a pivotal role in this process, whereas first-order interactions alone are insufficient to induce Turing instability. Specifically, higher-order interactions contribute to a transition from regions of high abundance to regions of low abundance. In addition, the mean-field approximation offers critical insights into the mechanism by which higher-order interactions induce Turing instabilities, primarily by increasing the nodes’ degrees within the network. Meanwhile, the findings underscore that higher-order interactions play a pivotal role in enhancing the stability of ecological community dynamics through the facilitation of pattern formation. This highlights the crucial importance of higher-order interactions in sustaining ecosystem diversity and stability.