{"title":"用算法复杂度的方法检验狼数时间序列的确定性成分","authors":"N. G. Makarenko, D. M. Volobuev, A. S. Rybintsev","doi":"10.1134/S0016793224700440","DOIUrl":null,"url":null,"abstract":"<p>This article discusses the testing of the complexity of the instrumental series of Wolf numbers. The work is initiated by the hypothesis of the existence of a low-dimensional dynamo as a model of the Sun’s magnetic activity. This mechanism produces the observable, in the Takens sense, as a broadband chaotic signal with a dominant 11-year mode (Frick et al., 2022). The time series of Wolf numbers is claimed to be this signal. In this article, we consider two problems. In the first, we describe a method for obtaining the average cycle for the dominant 11-year mode. It is based on the Fisher–Rao metric and the quantum mechanical analog of “probability amplitudes” for cycles. In the second problem, we investigate the algorithmic complexity of the instrumental series of Wolf numbers (SSN2) compared with surrogate data obtained by fractal mixing of this series. The mixing “whitens” the 11-year cycle but retains tuples of 2–3 monthly mean counts. Complexity was estimated as permutation entropy (Bandt et al., 2002). It was hypothesized that if the dominant mode was chaotic in nature, the complexity of the source and surrogate series would be close. Our results do not contradict the hypothesis of a chaotic signal with a single prevalent mode as a time series model of Wolf numbers.</p>","PeriodicalId":55597,"journal":{"name":"Geomagnetism and Aeronomy","volume":"64 8","pages":"1318 - 1327"},"PeriodicalIF":0.7000,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Testing the Deterministic Component of the Time Series of Wolf Numbers by Methods of Algorithmic Complexity\",\"authors\":\"N. G. Makarenko, D. M. Volobuev, A. S. Rybintsev\",\"doi\":\"10.1134/S0016793224700440\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This article discusses the testing of the complexity of the instrumental series of Wolf numbers. The work is initiated by the hypothesis of the existence of a low-dimensional dynamo as a model of the Sun’s magnetic activity. This mechanism produces the observable, in the Takens sense, as a broadband chaotic signal with a dominant 11-year mode (Frick et al., 2022). The time series of Wolf numbers is claimed to be this signal. In this article, we consider two problems. In the first, we describe a method for obtaining the average cycle for the dominant 11-year mode. It is based on the Fisher–Rao metric and the quantum mechanical analog of “probability amplitudes” for cycles. In the second problem, we investigate the algorithmic complexity of the instrumental series of Wolf numbers (SSN2) compared with surrogate data obtained by fractal mixing of this series. The mixing “whitens” the 11-year cycle but retains tuples of 2–3 monthly mean counts. Complexity was estimated as permutation entropy (Bandt et al., 2002). It was hypothesized that if the dominant mode was chaotic in nature, the complexity of the source and surrogate series would be close. Our results do not contradict the hypothesis of a chaotic signal with a single prevalent mode as a time series model of Wolf numbers.</p>\",\"PeriodicalId\":55597,\"journal\":{\"name\":\"Geomagnetism and Aeronomy\",\"volume\":\"64 8\",\"pages\":\"1318 - 1327\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-02-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geomagnetism and Aeronomy\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0016793224700440\",\"RegionNum\":4,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"GEOCHEMISTRY & GEOPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geomagnetism and Aeronomy","FirstCategoryId":"89","ListUrlMain":"https://link.springer.com/article/10.1134/S0016793224700440","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0
摘要
本文讨论了工具性沃尔夫数序列复杂性的检验。这项工作是由存在一个低维发电机作为太阳磁场活动模型的假设发起的。这种机制产生了Takens意义上的可观测值,即具有11年主导模式的宽带混沌信号(Frick et al., 2022)。沃尔夫数的时间序列被认为是这个信号。在本文中,我们考虑两个问题。首先,我们描述了一种获取主导11年模态平均周期的方法。它基于Fisher-Rao度规和周期“概率振幅”的量子力学模拟。在第二个问题中,我们研究了Wolf数仪器序列(SSN2)的算法复杂度,并与该序列通过分形混合获得的替代数据进行了比较。这种混合“漂白”了11年周期,但保留了2-3个月平均计数的元组。复杂性被估计为排列熵(Bandt et al., 2002)。假设如果主导模态本质上是混沌的,源序列和替代序列的复杂性将接近。我们的结果并不与混沌信号的单一流行模式作为沃尔夫数的时间序列模型的假设相矛盾。
Testing the Deterministic Component of the Time Series of Wolf Numbers by Methods of Algorithmic Complexity
This article discusses the testing of the complexity of the instrumental series of Wolf numbers. The work is initiated by the hypothesis of the existence of a low-dimensional dynamo as a model of the Sun’s magnetic activity. This mechanism produces the observable, in the Takens sense, as a broadband chaotic signal with a dominant 11-year mode (Frick et al., 2022). The time series of Wolf numbers is claimed to be this signal. In this article, we consider two problems. In the first, we describe a method for obtaining the average cycle for the dominant 11-year mode. It is based on the Fisher–Rao metric and the quantum mechanical analog of “probability amplitudes” for cycles. In the second problem, we investigate the algorithmic complexity of the instrumental series of Wolf numbers (SSN2) compared with surrogate data obtained by fractal mixing of this series. The mixing “whitens” the 11-year cycle but retains tuples of 2–3 monthly mean counts. Complexity was estimated as permutation entropy (Bandt et al., 2002). It was hypothesized that if the dominant mode was chaotic in nature, the complexity of the source and surrogate series would be close. Our results do not contradict the hypothesis of a chaotic signal with a single prevalent mode as a time series model of Wolf numbers.
期刊介绍:
Geomagnetism and Aeronomy is a bimonthly periodical that covers the fields of interplanetary space; geoeffective solar events; the magnetosphere; the ionosphere; the upper and middle atmosphere; the action of solar variability and activity on atmospheric parameters and climate; the main magnetic field and its secular variations, excursion, and inversion; and other related topics.