Global dynamic analysis of the North Pacific Ocean by data-driven generalized cell mapping method
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Global dynamic analysis of the North Pacific Ocean by data-driven generalized cell mapping method Zigang Li1 · Lulu Qiao1 · Jun Jiang2 · Ling Hong2 · Jian-Qiao Sun3 Received: 22 June 2020 / Revised: 1 August 2020 / Accepted: 14 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A data-driven generalized cell mapping method devoting to conquer the difficulty that how to carry out the global analysis for a model-free and complex system, without prior knowledge of the underlying system, is proposed in this paper to uncover the hidden flow structure existing in the North Pacific Ocean. By this way, the transient attracting region near the 30 degrees north latitude, acting as a short-term attractor in the North Pacific Ocean, is unveiled by investigating the topology of the seasonaware transition probability matrix created from the historical data bank of drifters. The predicted probability distributions of drifters are presented to illustrate the evolutions and concentration of ocean currents, which coincides with the real responses of drifters. Furthermore, the purpose of this paper is also to promote the applications of the data-driven cell mapping method in practical engineering. Keywords Data-driven analysis · Generalized cell mapping · Global dynamics · Ocean dynamics
1 Introduction The global analysis for a dynamic system aims to capture the intrinsic structures underlying the system, involving investigations of attractors and their basins of attraction, unstable invariant limit sets, and their stable and unstable manifolds, in order to gain an insight into the dynamic behaviors and the response characteristics of many engineering systems [1]. Traditionally, the global analysis is carried out on the base of an available model that is typically analytic, and the
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Jian-Qiao Sun [email protected] Zigang Li [email protected] Jun Jiang [email protected] Ling Hong [email protected]
1
Department of Mechanics, Xi’an University of Science and Technology, Xi’an 710054, People’s Republic of China
2
State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
3
Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA 95343, USA
correctness of the analysis relies on the model of system and accuracy of numerical computing. In real world applications, unfortunately, it is very hard or even impossible to construct an accurate model of complex system such as the ocean system, with a limited degree of freedom. It is quite often that we only have a series of input–output measurements. Thus, how to conduct the global analysis, without the knowledge of the model by using the measured data only, is a significant research with the needs of practical engineering. The generalized cell mapping (GCM for short) method is a powerful numerical technique, was pioneered by Hsu [2] in the 1980s, to explore the global structures for deterministic [3] or stochastic system [4]. The key of th
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