### Abstract

The dynamics of either associative or hierarchical neural network can boil down to the discovery of fixed point or contraction to the already established fixed point in a discrete dynamical system, and strict mathematical calculations have already proven this point. In other words, the dynamics of all types of neural network can be analyzed and explained by using the fixed point theory in the traditional discrete dynamical system. What is equally important is that the explanation and classification of chaos can also be expressed in terms of its relationship with fixed points. This has provided an important link between chaos and neural network in the traditional discrete dynamical system, namely, the fixed point theory. Based on this idea, this paper proposes a method to combine chaos with neural network using the fixed point theory. With a view to practical application, the paper provides several examples on improving pattern recognition ability by adding chaotic noise in learning machines as well as on improving the ability of optimal solution in the large by creating a new Chaotic Hopfield Neural Network. The approach proposed by this paper is proved user friendly and universally applicable through lab experiments of pattern recognition and solution of the Traveling Salesman Problem on a set of 100 cities.

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

Pages (from-to) | 645-648 |

Number of pages | 4 |

Journal | Unknown Journal |

Volume | 1 |

Publication status | Published - 1997 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Unknown Journal*,

*1*, 645-648.

**Method to combine chaos and neural network based on the fixed point theory.** / Zhou, D.; Yasuda, K.; Yokoyama, R.

Research output: Contribution to journal › Article

*Unknown Journal*, vol. 1, pp. 645-648.

}

TY - JOUR

T1 - Method to combine chaos and neural network based on the fixed point theory

AU - Zhou, D.

AU - Yasuda, K.

AU - Yokoyama, R.

PY - 1997

Y1 - 1997

N2 - The dynamics of either associative or hierarchical neural network can boil down to the discovery of fixed point or contraction to the already established fixed point in a discrete dynamical system, and strict mathematical calculations have already proven this point. In other words, the dynamics of all types of neural network can be analyzed and explained by using the fixed point theory in the traditional discrete dynamical system. What is equally important is that the explanation and classification of chaos can also be expressed in terms of its relationship with fixed points. This has provided an important link between chaos and neural network in the traditional discrete dynamical system, namely, the fixed point theory. Based on this idea, this paper proposes a method to combine chaos with neural network using the fixed point theory. With a view to practical application, the paper provides several examples on improving pattern recognition ability by adding chaotic noise in learning machines as well as on improving the ability of optimal solution in the large by creating a new Chaotic Hopfield Neural Network. The approach proposed by this paper is proved user friendly and universally applicable through lab experiments of pattern recognition and solution of the Traveling Salesman Problem on a set of 100 cities.

AB - The dynamics of either associative or hierarchical neural network can boil down to the discovery of fixed point or contraction to the already established fixed point in a discrete dynamical system, and strict mathematical calculations have already proven this point. In other words, the dynamics of all types of neural network can be analyzed and explained by using the fixed point theory in the traditional discrete dynamical system. What is equally important is that the explanation and classification of chaos can also be expressed in terms of its relationship with fixed points. This has provided an important link between chaos and neural network in the traditional discrete dynamical system, namely, the fixed point theory. Based on this idea, this paper proposes a method to combine chaos with neural network using the fixed point theory. With a view to practical application, the paper provides several examples on improving pattern recognition ability by adding chaotic noise in learning machines as well as on improving the ability of optimal solution in the large by creating a new Chaotic Hopfield Neural Network. The approach proposed by this paper is proved user friendly and universally applicable through lab experiments of pattern recognition and solution of the Traveling Salesman Problem on a set of 100 cities.

UR - http://www.scopus.com/inward/record.url?scp=0030661071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030661071&partnerID=8YFLogxK

M3 - Article

VL - 1

SP - 645

EP - 648

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -