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This paper deals with the identification of system equation of the chaotic dynamics by using smaller number of data based upon the genetic programming (GP). The problem to estimate the system equation from the chaotic data is important to analyze the structure of dynamics in the fields such as the business and economics. Especially, for the prediction of chaotic dynamics, if the number of data is restricted, we can not use conventional numerical method such as the linear-reconstruction of attractors and the prediction by using the neural networks. In this paper we utilize an efficient method to identify the system equation by using the GP. In the GP, the performance (fitness) of each individual is defined as the inversion of the root mean square error of the spectrum obtained by the original and predicted time series to suppress the effect of the initial value of variables. Conventional GA (Genetic Algorithm) is combined to optimize the constants in equations and to select the primitives in the GP representation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. The crossover operation used here means the replacement of a part of tree in individual A by a part of tree in individual B. To avoid the meaningless genetic operation, the validity of prefix representation of the subtree to be embedded to the other tree is probed by using the stack count. These newly generated individuals replace old individuals with lower fitness. The mutation operation is also used to avoid the convergence to the local minimum. In the simulation study, the identification method is applied at first to the well known chaotic dynamics such as the Logistic map and the Henon map. Then, the method is applied to the identification of the chaotic data of various time series by using one dimensional and higher dimensional system. The result shows better prediction than conventional ones in cases where the number of data is small.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.8 pp.1599-1607

- Publication Date
- 2000/08/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Digital Signal Processing)

- Category
- Nonlinear Signal Processing

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Yoshikazu IKEDA, Shozo TOKINAGA, "Approximation of Chaotic Dynamics by Using Smaller Number of Data Based upon the Genetic Programming and Its Applications" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 8, pp. 1599-1607, August 2000, doi: .

Abstract: This paper deals with the identification of system equation of the chaotic dynamics by using smaller number of data based upon the genetic programming (GP). The problem to estimate the system equation from the chaotic data is important to analyze the structure of dynamics in the fields such as the business and economics. Especially, for the prediction of chaotic dynamics, if the number of data is restricted, we can not use conventional numerical method such as the linear-reconstruction of attractors and the prediction by using the neural networks. In this paper we utilize an efficient method to identify the system equation by using the GP. In the GP, the performance (fitness) of each individual is defined as the inversion of the root mean square error of the spectrum obtained by the original and predicted time series to suppress the effect of the initial value of variables. Conventional GA (Genetic Algorithm) is combined to optimize the constants in equations and to select the primitives in the GP representation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. The crossover operation used here means the replacement of a part of tree in individual A by a part of tree in individual B. To avoid the meaningless genetic operation, the validity of prefix representation of the subtree to be embedded to the other tree is probed by using the stack count. These newly generated individuals replace old individuals with lower fitness. The mutation operation is also used to avoid the convergence to the local minimum. In the simulation study, the identification method is applied at first to the well known chaotic dynamics such as the Logistic map and the Henon map. Then, the method is applied to the identification of the chaotic data of various time series by using one dimensional and higher dimensional system. The result shows better prediction than conventional ones in cases where the number of data is small.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_8_1599/_p

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@ARTICLE{e83-a_8_1599,

author={Yoshikazu IKEDA, Shozo TOKINAGA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Approximation of Chaotic Dynamics by Using Smaller Number of Data Based upon the Genetic Programming and Its Applications},

year={2000},

volume={E83-A},

number={8},

pages={1599-1607},

abstract={This paper deals with the identification of system equation of the chaotic dynamics by using smaller number of data based upon the genetic programming (GP). The problem to estimate the system equation from the chaotic data is important to analyze the structure of dynamics in the fields such as the business and economics. Especially, for the prediction of chaotic dynamics, if the number of data is restricted, we can not use conventional numerical method such as the linear-reconstruction of attractors and the prediction by using the neural networks. In this paper we utilize an efficient method to identify the system equation by using the GP. In the GP, the performance (fitness) of each individual is defined as the inversion of the root mean square error of the spectrum obtained by the original and predicted time series to suppress the effect of the initial value of variables. Conventional GA (Genetic Algorithm) is combined to optimize the constants in equations and to select the primitives in the GP representation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. The crossover operation used here means the replacement of a part of tree in individual A by a part of tree in individual B. To avoid the meaningless genetic operation, the validity of prefix representation of the subtree to be embedded to the other tree is probed by using the stack count. These newly generated individuals replace old individuals with lower fitness. The mutation operation is also used to avoid the convergence to the local minimum. In the simulation study, the identification method is applied at first to the well known chaotic dynamics such as the Logistic map and the Henon map. Then, the method is applied to the identification of the chaotic data of various time series by using one dimensional and higher dimensional system. The result shows better prediction than conventional ones in cases where the number of data is small.},

keywords={},

doi={},

ISSN={},

month={August},}

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TY - JOUR

TI - Approximation of Chaotic Dynamics by Using Smaller Number of Data Based upon the Genetic Programming and Its Applications

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1599

EP - 1607

AU - Yoshikazu IKEDA

AU - Shozo TOKINAGA

PY - 2000

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E83-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2000

AB - This paper deals with the identification of system equation of the chaotic dynamics by using smaller number of data based upon the genetic programming (GP). The problem to estimate the system equation from the chaotic data is important to analyze the structure of dynamics in the fields such as the business and economics. Especially, for the prediction of chaotic dynamics, if the number of data is restricted, we can not use conventional numerical method such as the linear-reconstruction of attractors and the prediction by using the neural networks. In this paper we utilize an efficient method to identify the system equation by using the GP. In the GP, the performance (fitness) of each individual is defined as the inversion of the root mean square error of the spectrum obtained by the original and predicted time series to suppress the effect of the initial value of variables. Conventional GA (Genetic Algorithm) is combined to optimize the constants in equations and to select the primitives in the GP representation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. The crossover operation used here means the replacement of a part of tree in individual A by a part of tree in individual B. To avoid the meaningless genetic operation, the validity of prefix representation of the subtree to be embedded to the other tree is probed by using the stack count. These newly generated individuals replace old individuals with lower fitness. The mutation operation is also used to avoid the convergence to the local minimum. In the simulation study, the identification method is applied at first to the well known chaotic dynamics such as the Logistic map and the Henon map. Then, the method is applied to the identification of the chaotic data of various time series by using one dimensional and higher dimensional system. The result shows better prediction than conventional ones in cases where the number of data is small.

ER -