Abstract by David Reber
Dynamical Stability despite Time-Varying Network Structure
Dynamic processes on real-world networks are inherently time-delayed due to finite processing speeds, the need to transmit data over distances, or other interruptions in the network's dynamics.
These time-delays, which correspond to bisecting edges in the network's underlying graph of interactions, can and often do have a destabilizing effect on the network's dynamics.
We demonstrate that networks whose underlying graph of interactions satisfy the criteria which we refer to as intrinsic stability are able to maintain their stability even in the presence of time-varying time-delays.
These time-varying delays can be of any form, e.g. deterministic, stochastic, etc.
Furthermore, determining whether a network is intrinsically stable is straightforward and can be implemented on large-scale networks.