Abstract
This paper presents a new numerical method for computing global stable manifolds and global stable sets of nonlinear discrete dynamical systems. For a given map f:ℝd→ℝd, the proposed method is capable of yielding large parts of stable manifolds and sets within a certain compact region M⊂ℝd. The algorithm divides the region M in sets and uses an adaptive subdivision technique to approximate an outer covering of the manifolds. In contrast to similar approaches, the method requires neither the system’s inverse nor its Jacobian. Hence, it can also be applied to noninvertible and piecewise-smooth maps. The successful application of the method is illustrated by computation of one- and two-dimensional stable manifolds and global stable sets.
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Fundinger, D. Toward the Calculation of Higher-Dimensional Stable Manifolds and Stable Sets for Noninvertible and Piecewise-Smooth Maps. J Nonlinear Sci 18, 391–413 (2008). https://doi.org/10.1007/s00332-007-9016-4
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DOI: https://doi.org/10.1007/s00332-007-9016-4