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.
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© 2007 Springer
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Xu, W., He, Q., Li, S. (2007). The Cell Mapping Method for Approximating the Invariant Manifolds. In: Hu, H.Y., Kreuzer, E. (eds) Iutam Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty. IUTAM Book Series, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6332-9_12
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DOI: https://doi.org/10.1007/978-1-4020-6332-9_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6331-2
Online ISBN: 978-1-4020-6332-9
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