English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Topological stability criteria for networking dynamical systems with Hermitian Jacobian

MPS-Authors
/persons/resource/persons184459

Do,  Anne-Ly
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

Fulltext (public)
There are no public fulltexts available
Supplementary Material (public)
There is no public supplementary material available
Citation

Do, A.-L., Boccaletti, S., Epperlein, J., Siegmund, S., & Gross, T. (2016). Topological stability criteria for networking dynamical systems with Hermitian Jacobian. SI, 27(6), 888-903. doi:10.1017/S0956792516000425.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002C-32D4-8
Abstract
The central theme of complex systems research is to understand the emergent macroscopic properties of a system from the interplay of its microscopic constituents. The emergence of macroscopic properties is often intimately related to the structure of the microscopic interactions. Here, we present an analytical approach for deriving necessary conditions that an interaction network has to obey in order to support a given type of macroscopic behaviour. The approach is based on a graphical notation, which allows rewriting Jacobi's signature criterion in an interpretable form and which can be applied to many systems of symmetrically coupled units. The derived conditions pertain to structures on all scales, ranging from individual nodes to the interaction network as a whole. For the purpose of illustration, we consider the example of synchronization, specifically the (heterogeneous) Kuramoto model and an adaptive variant. The results complete and extend the previous analysis of Do et al. (2012 Phys. Rev. Lett. 108, 194102).