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Networks, which include nodes and connections, can help researchers model dynamic systems like the spread of disease or how the brain processes information.

Pairwise interactions between nodes can represent links between individuals—how two neurons connect with one another in the brain, for example—but scientists also study interactions involving three or more nodes. These higher-order interactions reveal changes and phenomena beyond those found by looking only at pairs.

Yuanzhao Zhang, an SFI Complexity Postdoctoral Fellow, has studied how higher-order interactions affect a system at small scales. In new work published in Science Advances, he reports on how higher-order interactions can reshape a system at larger, even global scales. "We wanted to know how they change the entire landscape," he says.

Zhang and his colleagues found that higher-order interactions can lead to deeper "basins of attraction," which are collections of starting points that end up at the same state as the system moves forward in time. If the system were a pendulum, the lowest point is an attractor, and every possible starting point is in the basin of attraction because they all eventually converge there.

If the system were a brain working through a complicated math problem, then the thought processes that lead to a solution—hopefully the correct one—are in the basin of attraction. A deeper basin means that the solutions are more stable—that is, starting points get to the bottom faster or more quickly recover from small perturbations.

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