@inproceedings{921b001eed6e4fd4bfa01aaceef159d2,
title = "The cell mapping method for approximating the invariant manifolds",
abstract = "The digraph cell mapping method (DCMM) is a powerful technique for global analysis of nonlinear systems. In this paper, we introduce two new notions to modify DCMM. After the modification, DCMM can successfully approximate the invariant manifolds of nonlinear systems. Furthermore, it is not only applicable to deterministic systems but also to stochastic systems. As an illustrative example, the safe basin erosion of a Duffing oscillator under deterministic or stochastic excitation is studied in detail. Numerical results show that the modified digraph cell mapping method (MDCMM) is an efficient tool to approximate the invariant manifolds of dynamical systems.",
keywords = "The invariant manifolds, The modified digraph cell mapping method",
author = "W. Xu and Q. He and S. Li",
year = "2007",
doi = "10.1007/978-1-4020-6332-9_12",
language = "英语",
isbn = "9781402063312",
series = "Solid Mechanics and its Applications",
publisher = "Springer Verlag",
pages = "117--126",
booktitle = "IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty - Proceedings of the IUTAM Symposium",
note = "IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty ; Conference date: 18-09-2006 Through 22-09-2006",
}