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A Graph Isomorphism Condition and Equivalence of Reaction Systems.

Daniela Genova1, Hendrik Jan Hoogeboom2, Nataša Jonoska3

  • 1Department of Mathematics and Statistics, University of North Florida, Jacksonville, USA.

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|February 11, 2020
PubMed
Summary

This study introduces a graph-based method to determine the equivalence of reaction systems. We define a unique graph representation called a skeleton, enabling efficient comparison of system dynamics.

Keywords:
directed graphsdynamics of reaction systemsequivalence of reaction systemsgraph isomorphismgraphs on posets

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Area of Science:

  • Theoretical Computer Science
  • Dynamical Systems Theory

Background:

  • Reaction systems model complex dynamic processes.
  • Equivalence of reaction systems is typically determined by isomorphic transition graphs.
  • Existing methods for graph isomorphism can be computationally intensive.

Purpose of the Study:

  • To introduce a novel graph representation, the skeleton, for reaction system dynamics.
  • To establish conditions for determining the isomorphism of skeletons.
  • To provide a new criterion for reaction system equivalence.

Main Methods:

  • Defining the 'skeleton' as a unique graph representation (a one-out graph) for reaction system dynamics.
  • Developing necessary and sufficient conditions for skeleton isomorphism.
  • Relating skeleton isomorphism back to the isomorphism of transition graphs.

Main Results:

  • The skeleton uniquely determines a directed graph.
  • We provide precise conditions for two skeletons to define isomorphic graphs.
  • This leads to a necessary and sufficient condition for reaction system equivalence.

Conclusions:

  • The skeleton provides an efficient method for comparing reaction system dynamics.
  • This work characterizes directed graphs corresponding to global dynamics of reaction systems.
  • The findings offer a new perspective on understanding and analyzing complex systems.