A New Interpolation Criterion for Computation of Two-Dimensional Manifolds
In this paper, a multi-threshold criterion was proposed for computation of two-dimensional manifolds. By taking the minimum threshold as the reference standard, thresholds are adapted according to the corresponding growth rate in dif-ferent directions. With the study of distance changes between adjacent orbits, prior knowledge can be got and used to guide the current interpolation to prepare data for the next loop. Minimum threshold reflects details of the manifold structure. To meet the geometric scale of current loop in processing of the computation of mani-fold, the size of minimum threshold is required to be proportional to the size of the loop. Ratio is recorded as the control factor. Due to the introduction of control fac-tor, the changes of thresholds can adapt to the changes of manifold better, and the structure of manifold can be constructed in different geometric scales. Lorenz sys-tem and Duffing system are taken as examples to demonstrate the effectiveness of the proposed approach.
KeywordsUnstable Manifold Base Manifold Geometric Scale Duffing System Adjacent Orbit
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