## Abstract

The paper promotes the study of computational aspects, primarily the convergence rate, of nonlinear dynamical systems from a combinatorial perspective. The authors identify the class of symmetric quadratic systems. Such systems have been widely used to model phenomena in the natural sciences, and also provide an appropriate framework for the study of genetic algorithms in combinatorial optimisation. They prove several fundamental general properties of these systems, notably that every trajectory converges to a fixed point. They go on to give a detailed analysis of a quadratic system defined in a natural way on probability distributions over the set of matchings in a graph. In particular, they prove that convergence to the limit requires only polynomial time when the graph is a tree. This result demonstrates that such systems, though nonlinear, are amenable to quantitative analysis.

Original language | English |
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Title of host publication | Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |

Publisher | IEEE Computer Society |

Pages | 304-313 |

Number of pages | 10 |

ISBN (Electronic) | 0818629002 |

DOIs | |

State | Published - 1992 |

Externally published | Yes |

Event | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States Duration: 24 Oct 1992 → 27 Oct 1992 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 1992-October |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |
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Country/Territory | United States |

City | Pittsburgh |

Period | 24/10/92 → 27/10/92 |

### Bibliographical note

Publisher Copyright:© 1992 IEEE.

## ASJC Scopus subject areas

- General Computer Science