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Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussianα-stable Lévy noise

Chinese Physics B 2023年第5期32卷 337-342页

作者：陆凌弘志李扬刘先斌 State Key Laboratory of Mechanics and Control for Mechanical Structures College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjing 210016China School of Automation Nanjing University of Science and TechnologyNanjing 210094China

Massive data from observations,experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these *** present a novel method to identify such high dimensional stochastic dynamical systems that are perturbed by a non-Gaussianα-stable Lévy *** explicitly,firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of nonlocal Kramers–Moyal *** the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the *** examples are then given to demonstrate the *** approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood transition path or mean exit time of these stochastic systems.

关键词： data-driven modelling noise-induced transitions Lévy noise Kramers–Moyal formuas

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Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment

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Chinese Physics B 2023年第5期32卷 343-349页

作者：刘蓉马万彪 School of Mathematics and Physics University of Science and Technology BeijingBeijing 100083China School of Science Chongqing University of Posts and TelecommunicationsChongqing 400065China

The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential equation model is constructed to describe the continuous culture of microorganisms with multiple nutrients and the flocculation process of microorganisms. The study of the dynamics of this model can provide feasible control strategies for the collection/extraction of microorganisms. The main theoretical results are sufficient conditions for the permanence and extinction of the stochastic differential equation model, which are also extensions of some results in the existing literatures. In addition, through numerical simulations, we vividly demonstrate the statistical characteristics of the stochastic differential equation model.

关键词： stochastic process stochastically ultimately bounded stochastic permanence noise-induced transitions

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