Master Stability Function approach to meta-networks

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The concept of networks has been very useful for investigating complex systems. By extending the network paradigm to systems with different interwoven classes of nodes, a much wider ensemble of complex systems has become accessible to scientific analysis. In order to better understand such meta-networks, the development of theoretical tools is indespensible. We have extended the Master Stability function formalism used in the study of coupled oscillators to the linear stability of meta-networks. This enabled us to decouple the influence of the two classes of subnetworks on the stability of the system, thus gaining a deeper analytical understanding of these systems. Furthermore, this greatly simplifies numerical evaluations, allowing to study much larger systems. In the meantime, we succeded in developing this formalism further in several directions, so that it can be applied to systems that contain several types of spatial nodes or species that perceive different spatial networks.Based on this newly developed toolbox we want to investigate in this project thestability and pattern-forming properties of different classes of metanetworks, and to extend the formalism even further. The systems to be investigated are spatially coupled foodwebs, ecosystems with sources and sinks, mutualistic and competitive networks on a spatial habitat network, or gene expression networks coupled by cell-cell communication. The questions to be addressed by this project include the influence of biomass flux on the stability of source-sink systems, the relevance of spatial structure for the switching between mutualistic and antagonistic species interactions, and the construction of genereulatory networks that display a Turing instability that leads to a desired pattern.