IJPAM: Volume 73, No. 3 (2011)

DETECTION OF CHANGE IN NON-LINEAR DYNAMICS
BEHIND THE PERIODIC TIME SERIES AND ITS
APPLICATION TO SOLAR CYCLE PREDICTION

Tetsuji Hidaka$^{1,2}$
$^1$Hakuhodo Inc.
5-3-1 Akasaka, Minato-Ku
Tokyo, 107-6322, JAPAN
$^2$Graduate School of Advanced Mathematical Sciences
Meiji University
1-1-1 Higashimita, Tamaku, Kawasaki, 214-8571, JAPAN


Abstract. This paper proposes a method for detecting a change in non-linear dynamics behind periodic time series. In order to develop this method, we define the smoothed pseudo determinacy function (SPDF) based on the theory of KM$_{2}$O-Langevin equations. Because SPDF has information about non-linear dynamics, the proposed method detects a change in non-linear dynamics in comparison to previous methods such as Time-Frequency Analysis and Wavelet Analysis. We confirmed its practicality by applying the method to monthly sunspot number. The result shows that one of the changes in non-linear dynamics at year 2004 is detected and the dynamics is changing into the same as ``Dalton Minimum" from year 1790 to 1820. From this result, we suggest that maximum of the next cycle will be as same as ``Dalton Minimum". This result supports some previous works.

Received: October 28, 2011

AMS Subject Classification: 62M10, 62M15

Key Words and Phrases: time series, non-linear, periodicity, sunspot, solar cycle prediction

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 3