Effect of higher-order interactions on tipping cascades on complex networks

Abstract: Tipping points are critical thresholds of parameters where tiny perturbations can lead to abrupt and large qualitative changes in the systems. Many real-world systems that exhibit tipping behavior can be represented as networks of interacting multistable units, such as vegetation patches or infrastructure networks, undergoing both pairwise and higher-order interactions. In this article, we explore how higher-order interactions shape the dynamics of tipping cascades in a conceptual system with tipping points. Numerical simulations on random, scale-free, and small-world networks reveal that higher-order interactions can induce cascades even at coupling strengths, where only pairwise interactions fail to do so. We also investigate the interplay of the pairwise and higher-order coupling strengths in random networks and illustrate the route to cascades through bifurcation diagrams. These results have also been demonstrated on real-world social networks. Apart from this, we show that repulsive higher-order interactions suppress tipping cascades at coupling strengths where pairwise interactions would cause them, and shift the cascade route from a saddle-node to a supercritical pitchfork bifurcation. Our results highlight the critical role of higher-order interactions in shaping cascade dynamics, offering insights for anticipating and mitigating critical transitions in ecosystems, climate systems, and socio-technical infrastructures.