Synchronization of Interconnected Systems with Applications to Biochemical Networks: an Input-Output Approach

TL;DR

This paper develops input-output based synchronization conditions for interconnected nonlinear systems, with applications to biochemical networks and cellular signaling, combining structural network information with subsystem properties.

Contribution

It introduces a novel input-output framework for analyzing synchronization in complex biochemical and cellular networks, including state-space models and oscillator networks.

Findings

Synchronization conditions derived for biochemical networks.

Application to Goodwin oscillator networks.

Framework applicable to both state-space and input-output models.

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 L2 space and referred to as a "species''. The compartments are, in turn, coupled through a diffusion-like term among the respective species. The synchronization conditions are provided by combining the input-output properties of the subsystems with information about the structure of 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 interactions of species, and externally, through intercellular signaling. The theory is illustrated providing synchronization conditions for networks of Goodwin oscillators.