### Abstract

Recently a sufficient condition for the recurrent neural network with the piecewise-linear output characteristic to generate a prescribed periodic sequence of binary vectors such that every two consecutive vectors differ in exactly one component has been derived. If a recurrent neural network satisfies this condition, it is guaranteed that any state trajectory of the network passes through the periodic sequence of regions corresponding to the periodic sequence of binary vectors. However, the asymptotic behavior of the state trajectories has not been clarified yet. In this paper, we study asymptotic behavior of state trajectories of recurrent neural networks satisfying the above-mentioned sufficient condition, and derive a criterion for state trajectories to converge a unique limit cycle.

Original language | English |
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Title of host publication | Proceedings of the International Joint Conference on Neural Networks |

Pages | 484-489 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2008 |

Externally published | Yes |

Event | 2008 International Joint Conference on Neural Networks, IJCNN 2008 - Hong Kong, China Duration: Jun 1 2008 → Jun 8 2008 |

### Other

Other | 2008 International Joint Conference on Neural Networks, IJCNN 2008 |
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Country | China |

City | Hong Kong |

Period | 6/1/08 → 6/8/08 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Artificial Intelligence

### Cite this

*Proceedings of the International Joint Conference on Neural Networks*(pp. 484-489). [4633836] https://doi.org/10.1109/IJCNN.2008.4633836

**On asymptotic behavior of state trajectories of piecewise-linear recurrent neural networks generating periodic sequence of binary vectors.** / Takahashi, Norikazu; Minetoma, Yasuhiro.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the International Joint Conference on Neural Networks.*, 4633836, pp. 484-489, 2008 International Joint Conference on Neural Networks, IJCNN 2008, Hong Kong, China, 6/1/08. https://doi.org/10.1109/IJCNN.2008.4633836

}

TY - GEN

T1 - On asymptotic behavior of state trajectories of piecewise-linear recurrent neural networks generating periodic sequence of binary vectors

AU - Takahashi, Norikazu

AU - Minetoma, Yasuhiro

PY - 2008

Y1 - 2008

N2 - Recently a sufficient condition for the recurrent neural network with the piecewise-linear output characteristic to generate a prescribed periodic sequence of binary vectors such that every two consecutive vectors differ in exactly one component has been derived. If a recurrent neural network satisfies this condition, it is guaranteed that any state trajectory of the network passes through the periodic sequence of regions corresponding to the periodic sequence of binary vectors. However, the asymptotic behavior of the state trajectories has not been clarified yet. In this paper, we study asymptotic behavior of state trajectories of recurrent neural networks satisfying the above-mentioned sufficient condition, and derive a criterion for state trajectories to converge a unique limit cycle.

AB - Recently a sufficient condition for the recurrent neural network with the piecewise-linear output characteristic to generate a prescribed periodic sequence of binary vectors such that every two consecutive vectors differ in exactly one component has been derived. If a recurrent neural network satisfies this condition, it is guaranteed that any state trajectory of the network passes through the periodic sequence of regions corresponding to the periodic sequence of binary vectors. However, the asymptotic behavior of the state trajectories has not been clarified yet. In this paper, we study asymptotic behavior of state trajectories of recurrent neural networks satisfying the above-mentioned sufficient condition, and derive a criterion for state trajectories to converge a unique limit cycle.

UR - http://www.scopus.com/inward/record.url?scp=56349087896&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56349087896&partnerID=8YFLogxK

U2 - 10.1109/IJCNN.2008.4633836

DO - 10.1109/IJCNN.2008.4633836

M3 - Conference contribution

SN - 9781424418213

SP - 484

EP - 489

BT - Proceedings of the International Joint Conference on Neural Networks

ER -