(Talk) Luca Scardovi, TUM - Analysis and Control of Synchronization in Nonlinear Interconnected Systems

Synchronization is the science of order in time and studies the ways rhythms become spontaneously organized. It is ubiquitous in nature and in engineering applications: groups of fireflies, neurons or pacemaker cells synchronize spontaneously; fish move in formations to escape predators and improve foraging; robots can coordinate to accomplish tasks more efficiently. In this talk I  will present a formalism to analyze synchronization in networks of dynamical systems where each component of the network (referred to as a “compartment”) itself consists of subsystems (referred to as “species”) represented as nonlinear operators. The input to the species includes the influence of other species within the compartment as well as a diffusion-like coupling term between identical species in different compartments.
The synchronization conditions are provided by combining the input-output properties of the subsystems with information about the structure of the network. The model is motivated by cellular networks where signaling occurs both internally, through interactions of species, and externally, through intercellular signaling. The theory is illustrated providing synchronization conditions for networks of genetic oscillators, neuronal models and convergence conditions for nonlinear state observers. If time permits I will also present a methodology to design dynamic controllers that overcome the limitations of static diffusive coupling for certain classes of dynamical systems.