Observation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability
Intercycle variations in the series of 11 yr solar activity cycles have a significant impact on both the space environment and climate. Whether solar cycle variability is dominated by deterministic chaos or stochastic perturbations remains an open question. Distinguishing between the two mechanisms...
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IOP Publishing
2025-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/adc72d |
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| author | Zi-Fan Wang Jie Jiang Jing-Xiu Wang |
| author_facet | Zi-Fan Wang Jie Jiang Jing-Xiu Wang |
| author_sort | Zi-Fan Wang |
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| description | Intercycle variations in the series of 11 yr solar activity cycles have a significant impact on both the space environment and climate. Whether solar cycle variability is dominated by deterministic chaos or stochastic perturbations remains an open question. Distinguishing between the two mechanisms is crucial for predicting solar cycles. Here we reduce the solar dynamo process responsible for the solar cycle to a one-dimensional iterative map, incorporating recent advances in the observed nonlinearity and stochasticity of the cycle. We demonstrate that deterministic chaos is absent in the nonlinear system, regardless of model parameters, if the generation of the poloidal field follows an increase-then-saturate pattern as the cycle strength increases. The synthesized solar cycles generated by the iterative map exhibit a probability density function (PDF) similar to that of observed normal cycles, supporting the dominant role of stochasticity in solar cycle variability. The parameters governing nonlinearity and stochasticity profoundly influence the PDF. The iterative map provides a quick and effective tool for predicting the range, including uncertainty, of the subsequent cycle strength when an ongoing cycle amplitude is known. Due to stochasticity, a solar cycle loses almost all its original information within one or two cycles. Although the simplicity of the iterative map, the behaviors it exhibits are generic for the nonlinear system. Our results provide guidelines for analyzing solar dynamo models in terms of chaos and stochasticity, highlight the limitations in predicting the solar cycle, and motivate further refinement of observational constraints on nonlinear and stochastic processes. |
| format | Article |
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| issn | 1538-4357 |
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| publishDate | 2025-01-01 |
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| spelling | doaj-art-ce5fdc6fd4704c6a9ed31b1cb40c18e82025-08-20T02:27:40ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-01984218310.3847/1538-4357/adc72dObservation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle VariabilityZi-Fan Wang0https://orcid.org/0000-0002-9455-9061Jie Jiang1https://orcid.org/0000-0001-5002-0577Jing-Xiu Wang2https://orcid.org/0000-0003-2544-9544State Key Laboratory of Solar Activity and Space Weather, NAOC, CAS, Beijing 100101, People’s Republic of China; School of Astronomy and Space Science, University of Chinese Academy of Sciences , Beijing, People’s Republic of ChinaSchool of Space and Earth Sciences, Beihang University , Beijing, People’s Republic of China; Key Laboratory of Space Environment Monitoring and Information Processing of MIIT , Beijing, People’s Republic of ChinaState Key Laboratory of Solar Activity and Space Weather, NAOC, CAS, Beijing 100101, People’s Republic of China; School of Astronomy and Space Science, University of Chinese Academy of Sciences , Beijing, People’s Republic of ChinaIntercycle variations in the series of 11 yr solar activity cycles have a significant impact on both the space environment and climate. Whether solar cycle variability is dominated by deterministic chaos or stochastic perturbations remains an open question. Distinguishing between the two mechanisms is crucial for predicting solar cycles. Here we reduce the solar dynamo process responsible for the solar cycle to a one-dimensional iterative map, incorporating recent advances in the observed nonlinearity and stochasticity of the cycle. We demonstrate that deterministic chaos is absent in the nonlinear system, regardless of model parameters, if the generation of the poloidal field follows an increase-then-saturate pattern as the cycle strength increases. The synthesized solar cycles generated by the iterative map exhibit a probability density function (PDF) similar to that of observed normal cycles, supporting the dominant role of stochasticity in solar cycle variability. The parameters governing nonlinearity and stochasticity profoundly influence the PDF. The iterative map provides a quick and effective tool for predicting the range, including uncertainty, of the subsequent cycle strength when an ongoing cycle amplitude is known. Due to stochasticity, a solar cycle loses almost all its original information within one or two cycles. Although the simplicity of the iterative map, the behaviors it exhibits are generic for the nonlinear system. Our results provide guidelines for analyzing solar dynamo models in terms of chaos and stochasticity, highlight the limitations in predicting the solar cycle, and motivate further refinement of observational constraints on nonlinear and stochastic processes.https://doi.org/10.3847/1538-4357/adc72dSolar cycleSolar dynamoSolar magnetic fieldsSolar active regions |
| spellingShingle | Zi-Fan Wang Jie Jiang Jing-Xiu Wang Observation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability The Astrophysical Journal Solar cycle Solar dynamo Solar magnetic fields Solar active regions |
| title | Observation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability |
| title_full | Observation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability |
| title_fullStr | Observation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability |
| title_full_unstemmed | Observation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability |
| title_short | Observation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability |
| title_sort | observation based iterative map for solar cycles i nature of solar cycle variability |
| topic | Solar cycle Solar dynamo Solar magnetic fields Solar active regions |
| url | https://doi.org/10.3847/1538-4357/adc72d |
| work_keys_str_mv | AT zifanwang observationbasediterativemapforsolarcyclesinatureofsolarcyclevariability AT jiejiang observationbasediterativemapforsolarcyclesinatureofsolarcyclevariability AT jingxiuwang observationbasediterativemapforsolarcyclesinatureofsolarcyclevariability |