BioND — Dynamics of Biological Networks

Fundamental nonlinear dynamics and data analysis

The central theme of our work is developing new approaches for understanding real-world complex systems. To develop powerful tools we build on modern concepts and insights form nonlinear dynamics and statistical physics. In turn our applied work inspires ideas for extending the mathematical foundations. In the past we have made several contributions to fundamental nonlinear dynamics and statistical physics. These include modeling approaches and algorithms from bifurcation detection and visualization.

Key Publications

Mesoscopic structures and the Laplacian spectra of random geometric graphs
Amy Nyberg, Thilo Gross, and Kevin E Bassler
Journal of Complex Networks 3(4), 543-551, 2015.
(abstract) (link to publisher) (arXiv) (download preprint)

Fusion of protein aggregates facilitates asymmetric damage segregation
Miguel Coelho, Stephen J. Lade, Simon Alberti, Thilo Gross, and Iva M. Tolic
PLoS Biology 12(6), e1001885, 2014.
(abstract) (link to publisher) (download preprint) (media coverage)

Graphical notation reveals topological stability criteria for collective dynamics in complex networks
Anne-Ly Do, Stefano Boccaletti, and Thilo Gross
Physical Review Letters 108(19), 194102-5, 2012.
(abstract) (link to publisher) (arXiv) (download preprint)

All scale-free networks are sparse
Charo I. del Genio, Thilo Gross, and Kevin E. Bassler
Physical Review Letters 107, 178701, 2011.
(abstract) (link to publisher) (arXiv) (download preprint) (media coverage)

Computation and visualization of bifurcation surfaces
Dirk Stiefs, Thilo Gross, Ralf Steuer, and Ulrike Feudel
International Journal Bifurcation and Chaos 18(8), 2191-2206, 2008.
(abstract) (link to publisher) (download preprint)

Generalized models as an universal approach to the analysis of nonlinear dynamical systems
Thilo Gross and Ulrike Feudel
Physical Review E 73, 016205-14, 2006.
(abstract) (link to publisher) (arXiv) (download preprint)

Analytical search for bifurcation surfaces in parameter space
Thilo Gross and Ulrike Feudel
Physica D 195(3-4), 292-302, 2004.
(abstract) (link to publisher) (download preprint)

Additional Publications

Hunting french ducks in a noisy environment
Nils Berglund, Barbara Gentz, and Christian Kuehn
Journal of Differential Equations 252, 4786–4841, 2012.
(abstract) (link to publisher) (arXiv) (download preprint)

Early warning signals for critical transitions: A generalized modeling approach
Steven J. Lade and Thilo Gross
PLoS Computational Biology 8, e1002360-6, 2012.
(abstract) (link to publisher) (arXiv) (download preprint) (media coverage)

Global return maps for mixed-mode oscillations with one fast and two slow variables
Christian Kuehn
Chaos 21, 033107, 2011.
(abstract) (link to publisher) (arXiv) (download preprint)

Weighted trade network in a model of preferential bipartite transactions
Abhijit Chakraborty and Subhrangshu S. Manna
Physical Review E 81, 016111-8, 2010.
(abstract) (link to publisher) (arXiv) (download preprint)

Recurrence networks – A novel paradigm for nonlinear time series analysis
Reik Donner, Yu Zou, Jonathan F. Donges, Norbert Marwan, and Jürgen Kurths
New Journal of Physics 12, 033025-40, 2010.
(abstract) (link to publisher) (arXiv) (download preprint)

Ambiguities in recurrence-based complex network representations of time series
Reik Donner, Yu Zou, Jonathan F. Donges, Norbert Marwan, and Jürgen Kurths
Physical Review E 81, 015101-4, 2010.
(abstract) (link to publisher) (arXiv) (download preprint)

Local dynamical equivalence of certain food webs
Thilo Gross and Ulrike Feudel
Ocean Dynamics 59(2), 417-427, 2009.
(abstract) (link to publisher) (arXiv) (download preprint)

Branching process in a stochastic extremal model
Subhrangshu S. Manna
Physical Review E 80, 021132-5, 2009.
(abstract) (link to publisher) (download preprint)

Robust oscillations in SIS epidemics on adaptive networks: Coarse graining by automated moment closure
Thilo Gross and Ioannis G. Kevrekidis
Europhysics Letters 82(3), 38004-6, 2008.
(abstract) (link to publisher) (arXiv) (download preprint) (media coverage)

Generalized models as an universal approach to the analysis of nonlinear dynamical systems
Thilo Gross and Ulrike Feudel
Physical Review E 73, 016205-14, 2006.
(abstract) (link to publisher) (arXiv) (download preprint)

Media Coverage

Roland G. Roberts, PloS Biology Synopsis, 2014-06-17
We all pass unwanted stuff on to our children—emotional baggage, peculiar habits, unfashionable furniture. Cells do the same thing when they divide; along with their newly replicated genomes andthe vital cellular organelles, they also pass on a lifetime’s worth of accrued rubbish. An important component of this is the legacy of insoluble aggregated protein that the parent cell has failed to deal with by the normal processes of degradation, and the amount that’s passed on can affect the lifespan and wellbeing of the daughter cells.
(more) (pdf)

Rachel Ehrenberg, ScienceNews, 2012-02-08
Math tools predict when systems are on the brink.
(more)

Tim Barribeau, io9, 2012-02-03
Predicting when a complex system will go through a sudden change is hard — either you need vast swathes of information, or you make rather bad predictions. But we want to spot critical transitions before they happen, regardless of whether we're talking about irreversible damage to coral reefs, stock market crashes, or fishery collapses.
(more)

Sitabhra Sinha, Physics, 2011-10-17
How nodes connect to each other may explain why we don’t see certain classes of networks.
(more)

Jan Lublinski, German Public Radio (Deutschlandfunk), 2009-07-06
Wie auch bei der Schweinegrippe, ist der Krankheitsverlauf des Dengue-Fiebers meist relativ harmlos. Dennoch stecken sich ganze Städte schnell mit dem Fieber an. Wie die Ausbreitung abläuft, untersuchen derzeit Wissenschaftler in Dresden - mit Hilfe von Mathematik
(more) (mp3 audio)