What it is
Earlier studies of network dynamics suggested that heterogeneity among nodes inhibits stability, which is at odds with how common inherently heterogeneous natural and engineered systems are. The authors show that this conclusion arises from model reductions introduced for mathematical tractability and breaks down when the dynamics of each node are higher-dimensional, which yields non-Hermitian Jacobians. In such systems, including neural, power-grid and material networks, heterogeneity among nodes can instead enhance stability, even when parameters are randomly disordered.
Why it matters
Real networks are heterogeneous almost everywhere, so a theory in which heterogeneity destabilizes them sat uneasily with the systems it describes. The authors trace the stabilizing effect to non-Hermiticity, which also underlies the stabilizing effects of heterogeneity in the network itself; those can arise even in one-dimensional node dynamics through nonreciprocal interactions, as shown for ecological networks. They conclude that disorder is not a liability but a general resource for stabilizing complex systems.
Every metric behind this entry is listed, with its source, under Sources and data below.
Filed underNeural Networks and Reservoir Computing, Advanced Graph Neural Networks, Neural dynamics and brain function