Global convergence of quorum-sensing networks

In many natural synchronization phenomena, communication between individual elements occurs not directly, but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in the environment which in turn are sensed and used for population coordination. Extending this motivation to a general non- linear dynamical system context, this paper analyzes synchronization phenomena in networks where communication and coupling between nodes are mediated by shared dynamical quan- tities, typically provided by the nodes' environment. Our model includes the case when the dynamics of the shared variables themselves cannot be neglected or indeed play a central part. Applications to examples from systems biology illustrate the approach.Comment: Version 2: minor editions, added section on noise. Number of pages: 36

Symmetries, Stability, and Control in Nonlinear Systems and Networks

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising e.g. in genetic networks, of invariance to environmental symmetries, and of imposing different patterns of synchrony in a network.Comment: 16 pages, second versio