Partial Synchronization and Model Reduction of Nonlinear Biological Networks

Yu Kawano, University of Groningen


The talk consists of two parts. In the first one, we study the partial synchronization of Kuramoto oscillators. Partial synchronization of neuronal ensembles are often observed in the human brain, which is believed to facilitate communication among anatomical regions demanded by cognitive tasks. Since such neurons are commonly modeled by oscillators, to better understand their partial synchronization behavior, we study partial phase cohesiveness in networks of Kuramoto oscillators. In the second part, we study model reduction of nonlinear monotone networks. Biological networks can easily be nonlinear and large scale. For simplification of analysis, it is reasonable to construct less complex models. In this talk, we focus on biological networks which can be modeled as monotone systems such as gene regulatory networks. Based on nice properties of monotone systems, we provide an empirical model reduction method for nonlinear monotone systems and then apply the proposed method to gene regulatory networks.