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Acta Informatica

, Volume 43, Issue 7, pp 501–519 | Cite as

Geometric analysis of nondeterminacy in dynamical systems

Towards a geometric analysis of concurrent systems
  • Rafael Wisniewski
  • Martin Raussen
Original article

Abstract

This article intends to provide some new insights into concurrency using ideas from the theory of dynamical systems. Inherently discrete concurrency corresponds to a parallel continuous concept: a discrete state space corresponds to a differential manifold, an execution path corresponds to a flow line of a dynamical system. To model non-determinacy within dynamical systems, we introduce a new geometrical object, a section cone. A section cone is a convex set in the space of vector fields, all elements having the same singular points. We show that it is enough to consider flow lines of a single vector field in order to capture the behavior of all flow lines in the section cone up to homotopy (corresponding to equivalence of executions).

Keywords

Singular Point Partial Order Stable Manifold Differential Inclusion Section Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Electronic SystemsAalborg UniversityAalborgDenmark
  2. 2.Department of Mathematical SciencesAalborg UniversityAalborgDenmark

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