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Network Control Analysis for Time-Dependent Dynamical States

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Dynamics, Games and Science II

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 2))

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Abstract

We present an approach to network control analysis that applies to some important time-dependent dynamical states for both autonomous and non-autonomous dynamical systems. In particular, the theory applies to periodic solutions of autonomous and periodically forced differential equations. The key results are summation theorems that substantially generalise previous results. These results can be interpreted as mathematical laws stating the need for a balance between fragility and robustness in such systems. We also present the theory behind what has been called global sensitivity analysis where sensitivities are defined in terms of principal components and principal control coefficients.

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Authors and Affiliations

  1. Warwick Systems Biology & Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    D. A. Rand

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  1. D. A. Rand
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Correspondence to D. A. Rand .

Editor information

Editors and Affiliations

  1. Pura e Aplicada (IMPA), Instituto de Matemática, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Rio de Janeiro, Brazil

    Mauricio Matos Peixoto

  2. Faculdade de Ciências, Departamento de Matemática, Universidade do Porto, Rua do Campo Alegre 687, Porto, 4169-007, Portugal

    Alberto Adrego Pinto

  3. Warwick Systems Biology, University of Warwick, Coventry House, Coventry, CV4 7AL, United Kingdom

    David A. Rand

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Rand, D.A. (2011). Network Control Analysis for Time-Dependent Dynamical States. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science II. Springer Proceedings in Mathematics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14788-3_1

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