A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics.

The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closed-form analytical solution for the calculation of a system's Jacobian from a time series.

Far-ranging generalist top predators enhance the stability of meta-foodwebs.

Identifying stabilizing factors in foodwebs is a long standing challenge with wide implications for community ecology and conservation. Here, we investigate the stability of spatially resolved meta-foodwebs with far-ranging super-predators for whom the whole meta-foodwebs appears to be a single habitat. By using a combination of generalized modeling with a master stability function approach, we are able to efficiently explore the asymptotic stability of large classes of realistic many-patch meta-foodwebs.

Master stability functions reveal diffusion-driven pattern formation in networks.

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space.