Noisy voter models in switching environments.

We study the stationary states of variants of the noisy voter model, subject to fluctuating parameters or external environments. Specifically, we consider scenarios in which the herding-to-noise ratio switches randomly and on different timescales between two values. We show that this can lead to a phase in which polarized and heterogeneous states exist. Second, we analyze a population of noisy voters subject to groups of external influencers, and show how multipeak stationary distributions emerge. Our work is based on a combination of individual-based simulations, analytical approximations in terms of a piecewise-deterministic Markov processes (PDMP), and on corrections to this process capturing intrinsic stochasticity in the linear-noise approximation. We also propose a numerical scheme to obtain the stationary distribution of PDMPs with three environmental states and linear velocity fields.

Lyapunov exponents for temporal networks.

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network and construct a measure to estimate the network maximum Lyapunov exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low- and high-dimensional chaos and finally discuss potential applications.