Untangling complex dynamical systems via derivative-variable correlations
- Inferring the internal interaction patterns of a complex dynamical system is a challenging problem. Traditional methods often rely on examining the correlations among the dynamical units. However, in systems such as transcription networks, one unit's variable is also correlated with the rate of change of another unit's variable. Inspired by this, we introduce the concept of derivative-variable correlation, and use it to design a new method of reconstructing complex systems (networks) from dynamical time series. Using a tunable observable as a parameter, the reconstruction of any system with known interaction functions is formulated via a simple matrix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length comparable to the characteristic dynamical time scale. Our method also provides a reliable precision estimate. We illustrate the method's implementation via elementary dynamical models, and demonstrate its robustness to both model error and observation error.
Author details: | Zoran Levnajic, Arkadij PikovskijORCiDGND |
---|---|
DOI: | https://doi.org/10.1038/srep05030 |
ISSN: | 2045-2322 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/24848769 |
Title of parent work (English): | Scientific reports |
Publisher: | Nature Publ. Group |
Place of publishing: | London |
Publication type: | Article |
Language: | English |
Year of first publication: | 2014 |
Publication year: | 2014 |
Release date: | 2017/03/27 |
Volume: | 4 |
Number of pages: | 6 |
Funding institution: | European Union [FISNM-3330-13-500033]; European Regional Development Fund; DFG [FOR868]; ARRS [P1-0383, J1-5454, L7-4119] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |
Publishing method: | Open Access |