Data-driven approach for extracting the most probable exit trajectory of stochastic dynamical systems with non-Gaussian Lévy noise
陆凌弘志 1李扬 2刘先斌1
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作者信息
1. State Key Laboratory of Mechanics and Control for Mechanical Structures,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China
2. School of Automation,Nanjing University of Science and Technology,Nanjing 210094,China
The burgeoning data-driven techniques endow large potential to predict fairly practical or complex dynamical systems in various fields through massive data.Lévy noise,a more universal and intricate fluctuation model comparing with Gaussian white noise,is widely employed in many non-Gaussian cases to mimic bursting or hopping.In this manuscript,we present a systematic data-driven method to identify the most probable exit trajectory of a system that is perturbed both by Gaussian white noise and non-Gaussian Lévy noise.The main theoretical and numerical conceptions involve a set of extended Kramers-Moyal formulas and the Kolmogorov forward equation in classic dynamical systems theory as well as a supervise learning theory to solve the fitting problems by using the Cross Validation.We then give two examples to show the feasibility in detail,and do a brief bi-furcation analysis for the most probable exit trajectory.The above approach will serve as a numerical correspondence to as well as verification for the relative theoretical research,and provide a referential resolution to the numerical identification of more transition indicators of this complex system,which is more general than the Gaussian diffusion process.
关键词
Rare random transitions/The most probable exit path/Non-local Kramers-Moyal formulas/Non-local Kolmogorov for-ward equation/Non-Gaussian noise pertubation
Key words
Rare random transitions/The most probable exit path/Non-local Kramers-Moyal formulas/Non-local Kolmogorov for-ward equation/Non-Gaussian noise pertubation
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