Reachability Algorithm for Biological Piecewise-Affine Hybrid Systems

  • Anil Aswani
  • Claire Tomlin
Conference paper

DOI: 10.1007/978-3-540-71493-4_49

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4416)
Cite this paper as:
Aswani A., Tomlin C. (2007) Reachability Algorithm for Biological Piecewise-Affine Hybrid Systems. In: Bemporad A., Bicchi A., Buttazzo G. (eds) Hybrid Systems: Computation and Control. HSCC 2007. Lecture Notes in Computer Science, vol 4416. Springer, Berlin, Heidelberg

Abstract

We consider a class of qualitative biological models which describe species (e.g. protein) interactions in terms of promotion or inhibition, from which a piecewise-affine (PWA) hybrid system model can be generated. These models have a special structure under which negative feedback is a necessary condition for the presence of limit cycles, centers, and foci. We describe modifications to reachability algorithms to take advantage of this special structure, and we give conditions on the qualitative model for termination of the algorithm. An example of applying the algorithm to a simple biological system is given.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Anil Aswani
    • 1
  • Claire Tomlin
    • 1
  1. 1.University of California at Berkeley, Dept. of Electrical Engineering and Computer Sciences 

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