Inhibition of explosive transitions in spreading dynamics by nonlinear higher-order adaptation

The coevolution of structure and dynamics, known as adaptation, is a fundamental property in various systems and drives diverse emergent behaviors. However, the adaptation in most works primarily stems from pairwise situations, which is insufficient to capture ubiquitous higher-order characteristics of real systems. Here, we introduce higher-order adaptation, characterized by baseline rewiring rate and nonlinear higher-order exponent, to model the coevolution of higher-order structure and spreading dynamics. We develop a hyperedge-based theoretical framework that well predicts critical behaviors and outbreak sizes. Notably, the inherent nonlinearity of higher-order adaptation inhibits bistability and explosive transitions, which is qualitatively opposite to the classical findings associated with pairwise adaptation or higher-order contagion. This inhibitory effect is enhanced by rewiring accuracy and remains robust across various adaptive spreading models. Our work establishes higher-order adaptation as a fundamentally distinct mechanism from pairwise adaptation, shedding light on adaptive systems.