@article{GrossFeudel2006,
  author    = {Gross, Thilo and Feudel, Ulrike},
  title     = {Generalized models as a universal approach to the analysis of nonlinear dynamical systems},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.73.016205},
  year      = {2006},
  abstract  = {We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socioeconomic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web},
  language  = {en}
}
@article{GrossD'LimaBlasius2006,
  author    = {Gross, Thilo and D'Lima, Carlos J. Dommar and Blasius, Bernd},
  title     = {Epidemic dynamics on an adaptive network},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.96.208701},
  year      = {2006},
  abstract  = {Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. This gives rise to assortative degree correlation, oscillations, hysteresis, and first order transitions. We propose a low-dimensional model to describe the system and present a full local bifurcation analysis. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications},
  language  = {en}
}
@article{SteuerGrossSelbigetal.2006,
  author    = {Steuer, Ralf and Gross, Thilo and Selbig, Joachim and Blasius, Bernd},
  title     = {Structural kinetic modeling of metabolic networks},
  series = {Proceedings of the National Academy of Sciences of the United States of America},
  volume    = {103},
  journal   = {Proceedings of the National Academy of Sciences of the United States of America},
  number    = {32},
  publisher = {National Academy of Sciences},
  address   = {Washington},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.0600013103},
  pages     = {11868 -- 11873},
  year      = {2006},
  abstract  = {To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a statistical exploration of the comprehensive parameter space. The method is exemplified on two paradigmatic metabolic systems: the glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.},
  language  = {en}
}