Complex systems are high-dimensional nonlinear dynamical systems with heterogeneous
interactions among their constituents. To make interpretable predictions about their large …

A network consists of two interdependent parts: the network topology or graph, consisting of
the links between nodes and the network dynamics, specified by some governing equations …

We investigate epidemic spreading in a deterministic susceptible-infected-susceptible
model on uncorrelated heterogeneous networks with higher-order interactions. We provide …

Network resilience is a fundamental property of many high-dimensional systems to maintain
their functions in the event of disturbances and errors. Despite substantial progress …

Many real-world complex systems, when hitting a tipping point, undergo irreversible sudden
shifts that can eventually take a great toll on humanity and the natural world, such as …

Dimension reduction is a common strategy to study nonlinear dynamical systems composed
by a large number of variables. The goal is to find a smaller version of the system whose …

Dimension reduction techniques for dynamical systems on networks are considered to
promote our understanding of the original high-dimensional dynamics. One strategy of …

Many complex dynamical systems in the real world, including ecological, climate, financial
and power-grid systems, often show critical transitions, or tipping points, in which the …

Successfully anticipating sudden major changes in complex systems is a practical concern.
Such complex systems often form a heterogeneous network, which may show multi-stage …

The spectral analysis of dynamical systems is a staple technique for analyzing a vast range
of systems. But beyond its analytical utility, it is also the primary lens through which many …