### Abstract

A neural network capable of retrieval of sequential patterns is analysed. The authors treat the network proposed by Buhmann and Schulten (1987). Although they concluded that the thermal noise induces retrieval of sequential patterns, the authors show that the network has limit cycle solutions even at zero temperature. Behaviour of the network at high temperatures is also analysed. The transition temperatures between a high-temperature fixed point phase and a limit cycle phase are calculated numerically to draw a phase diagram. The characteristic features of the phase diagram are discussed. The reentrant transition temperatures between the limit cycle and low-temperature fixed point phases are calculated analytically.

Original language | English |
---|---|

Article number | 024 |

Pages (from-to) | 4627-4641 |

Number of pages | 15 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 23 |

Issue number | 20 |

DOIs | |

Publication status | Published - 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*23*(20), 4627-4641. [024]. https://doi.org/10.1088/0305-4470/23/20/024

**Sequential retrieval of non-random patterns in a neural network.** / Nakamura, Tota; Nishimori, H.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 23, no. 20, 024, pp. 4627-4641. https://doi.org/10.1088/0305-4470/23/20/024

}

TY - JOUR

T1 - Sequential retrieval of non-random patterns in a neural network

AU - Nakamura, Tota

AU - Nishimori, H.

PY - 1990

Y1 - 1990

N2 - A neural network capable of retrieval of sequential patterns is analysed. The authors treat the network proposed by Buhmann and Schulten (1987). Although they concluded that the thermal noise induces retrieval of sequential patterns, the authors show that the network has limit cycle solutions even at zero temperature. Behaviour of the network at high temperatures is also analysed. The transition temperatures between a high-temperature fixed point phase and a limit cycle phase are calculated numerically to draw a phase diagram. The characteristic features of the phase diagram are discussed. The reentrant transition temperatures between the limit cycle and low-temperature fixed point phases are calculated analytically.

AB - A neural network capable of retrieval of sequential patterns is analysed. The authors treat the network proposed by Buhmann and Schulten (1987). Although they concluded that the thermal noise induces retrieval of sequential patterns, the authors show that the network has limit cycle solutions even at zero temperature. Behaviour of the network at high temperatures is also analysed. The transition temperatures between a high-temperature fixed point phase and a limit cycle phase are calculated numerically to draw a phase diagram. The characteristic features of the phase diagram are discussed. The reentrant transition temperatures between the limit cycle and low-temperature fixed point phases are calculated analytically.

UR - http://www.scopus.com/inward/record.url?scp=36149035086&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36149035086&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/23/20/024

DO - 10.1088/0305-4470/23/20/024

M3 - Article

VL - 23

SP - 4627

EP - 4641

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 20

M1 - 024

ER -