Synchronization of interconnected systems with applications to biochemical networks: An input-output approach

Abstract—This paper provides synchronization conditions for networks of nonlinear systems. The components of the network (referred to as “compartments ” in this paper) are made up of an identical interconnection of subsystems, each represented as an operator in an extended space and referred to as a “species.” The compartments are, in turn, coupled through a diffusion-like term among the respective species. The synchronization condi-tions are provided by combining the input-output properties of the subsystems with information about the structure of the network. The paper also explores results for state-space models, as well as biochemical applications. The work is motivated by cellular networks where signaling occurs both internally, through inter-actions of species, and externally, through intercellular signaling. The theory is illustrated by providing synchronization conditions for networks of Goodwin oscillators. Index Terms—Graph theory, interconnected systems, input-output stability, nonlinear systems, synchronization. I